nth term computed.
AskSia identifies a and r from the given terms, then plugs into a_n = a r^(n-1) and computes any term you need.
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AI Solver by AskSia
Geometric Progression Solver: every term and sum
Type or photograph any geometric progression problem. AskSia identifies the first term, the common ratio, and the index, then applies a_n = a r^(n-1) for terms, S_n = a(1-r^n)/(1-r) for partial sums, and a/(1-r) for infinite sums when convergent. Every step gets shown.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
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Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
What is a geometric progression?
A geometric progression (GP) is a sequence where each term equals the previous term times a constant called the common ratio. If the first term is a and the common ratio is r, the sequence is a, a*r, a*r^2, a*r^3, and so on. The nth term is a_n = a * r^(n-1). The sum of the first n terms is S_n = a * (1 - r^n) / (1 - r) when r is not 1. An infinite GP converges to a / (1 - r) when |r| < 1, and diverges otherwise.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why AskSia is built for GP problems.
Every formula stated, every value substituted, every sum checked for convergence.
Finite sums.
S_n = a(1-r^n)/(1-r) gets applied with values substituted. Special case r = 1 (just n*a) is handled separately.
Partial sum
Infinite sums when valid.
AskSia checks |r| < 1 before applying a/(1-r). If r is too large, divergence is reported, not a wrong number.
Convergence
Find common ratio.
Given two terms, divide the later by the earlier and adjust for index gap. AskSia handles this with full arithmetic.
Ratio
Connection to exponentials.
GPs and continuous exponentials are siblings. AskSia connects discrete GP to its continuous counterpart on request.
Concept
Word problem parsing.
Bouncing ball, depreciating asset, compound interest in discrete time. AskSia identifies the structure and applies the right formula.
Word problems
How It Works
Solve a GP problem in three steps.
Step 01
Enter what you know.
First term, common ratio, number of terms, specific terms, or partial sums. AskSia identifies the unknown.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia applies the formula.
Right formula picked based on what is asked. Values substituted. Arithmetic performed with every step shown.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the answer.
Final term, sum, ratio, or first term reported. For infinite sums, convergence is verified first.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
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Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
Where GPs show up.
Sequence problems.
Find the 20th term of a GP with first term 3 and ratio 2. AskSia applies 3 * 2^19 directly.
Sequence
Compound interest in discrete time.
Annual interest compounded n times forms a GP. AskSia computes the balance after any year.
Finance
Bouncing ball problems.
Ball rebounds to a fraction r of its previous height. Total distance is a finite or infinite GP sum.
Physics
Repeating decimal to fraction.
0.3 repeating = 3/10 + 3/100 + ... = (3/10)/(1 - 1/10) = 1/3. AskSia applies infinite GP sum.
Number theory
Fractal length.
Each iteration multiplies length by r. Total length is a GP sum. AskSia computes for any number of iterations.
Geometry
Word problems on tests.
SAT, ACT, AP Calculus all include GP problems. AskSia parses the wording and applies the right formula.
Test prep
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
What is the difference between an arithmetic and geometric progression?
An arithmetic progression adds a constant common difference each step: a, a+d, a+2d, and so on. A geometric progression multiplies by a constant common ratio each step: a, a*r, a*r^2, and so on. AP terms grow linearly; GP terms grow (or decay) exponentially. AskSia identifies which type a sequence is when given several consecutive terms.
When does an infinite geometric series converge?
When the absolute value of the common ratio is less than 1: |r| < 1. If |r| >= 1, the terms do not shrink fast enough and the sum diverges. AskSia checks the value of r before applying the infinite-sum formula a/(1-r). If r is on the boundary or exceeds it, the result is reported as divergent rather than a numerical answer.
How do I find the common ratio if I only have two non-consecutive terms?
If you know a_p and a_q with p < q, then a_q = a_p * r^(q-p), so r = (a_q / a_p)^(1/(q-p)). AskSia computes the index gap, divides, and takes the appropriate root. The sign of r is determined by whether terms alternate sign and the parity of the index gap.
Can a geometric progression have negative ratio?
Yes. If r is negative, the terms alternate sign: a, -a*|r|, a*r^2, -a*|r|^3, and so on. The formulas for nth term and sum still apply. AskSia handles negative ratios directly and notes the alternating pattern in the output. Infinite sums converge whenever |r| < 1, including negative r in (-1, 0).
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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Every term, every sum, every ratio.
Join 2M+ students using AskSia to solve geometric progressions step-by-step. nth term, partial sums, infinite sums with convergence check, and word problems handled.
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