QQuestion
The fourth term of a Geometric Progression (G.P.) is 16 and its seventh term is 128. Find its:
(a) common ratio
(b) first term
ICSEClass XMathematicsArithmetic And Geometric Progression03 Mark2026 Easy
✓Answer
For a G.P., nth term = arⁿ⁻¹.
Given,
Fourth term: ar³ = 16 …(1)
Seventh term: ar⁶ = 128 …(2)
(a) Dividing equation (2) by equation (1):
\frac{\mathrm{a}\mathrm{r}^{6}}{\mathrm{a}\mathrm{r}^{3}}=\frac{128}{16}⇒ r³ = 8
⇒ r = ∛8 = 2
Therefore, the common ratio is 2.
(b) Substituting r = 2 in equation (1):
a(2)³ = 16
⇒ 8a = 16
⇒ a = \frac{16}{8} = 2
Therefore, the first term is 2.
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