Class 9 · Chapter 8

Predicting What Comes Next: Sequences and Progressions

Arithmetic and geometric progressions, general terms, sums.

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Ganita Manjari · Class 9 (2026-27)

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Detailed theory

Fixed jump between consecutive terms.

2, 5, 8, 11, \ldots

has

a=2, d=3

. Nth term:

a + (n-1)d

Key concepts & formulas

**AP** (arithmetic): constant difference

d

;

a_n = a + (n-1)d

Sum of

n

AP terms:

S_n = \tfrac n2 [2a + (n-1)d]

**GP** (geometric): constant ratio

r

;

a_n = ar^{n-1}

Sum of GP:

S_n = a(r^n - 1)/(r-1)

for

r\ne 1

Recognise pattern before applying formula.