Question

Find the 10th term of GP whose 2nd term is 12 and 4th term is 27

Answer 1

The 10th term of G.P is 307.54.

Explanation:

Given: 2nd term, ar = 12 -----(1)

4th term, ar³ = 27----(2)

10th term = ?

Formula for G.P is a, ar, ar², ....

To find the nth term tₙ = $ar^{n-1}$

$\frac{ar^{3}}{ar}=\frac{27}{12}$

$r^{2}=\frac{9}{4}$

$r = \frac{3}{2}$

Substituting r in equation 1, we get

$a \times \frac{3}{2} =12$

a x 3 = 24

a = 8

The 10th term be a₁₀ = ar⁹

a₁₀ = 8 x $(\frac{3}{2} )^{9}$

= 8 x $\frac{19683}{512}$

= 8 x 38.44

= 307.54

The 10th term of G.P is 307.54.

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