Mixed AP–GP Series Solver

Mixed AP–GP Series Solver

Class 10 • Series that combine arithmetic and geometric patterns

Enter a series of at least 4 terms to analyse

Enter series

Examples

Result

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Pattern type—
Explicit formula—
Recursive form—
Next term—

Type A + B·rn−1

When first differences form a GP with ratio r, the original series is of the form:
an = A + B · rn−1
Example: 2, 4, 10, 28, 82 → differences 2, 6, 18, 54 (ratio 3) → an = 1 + 3n−1

AGP (Arithmetic–Geometric)

Terms of the form (a + (n−1)d) · rn−1:
a, (a+d)r, (a+2d)r2, (a+3d)r3, …
Also covered: pure AP, pure GP, and linear recurrence an+1 = p·an + q.

Step-by-step solution

1. Observe the series

  1. Enter a series and press Analyse.

2. First differences

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3. Identify the pattern

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4. Formula and next term

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NCERT Class 10 • Sequences and Series • Mixed AP–GP patterns