Question

If the 2nd and 5th terms of a GP are 24 and 81, respectively,
find the GP.

Answer 1

Answer:

the GP is

16, 24, 36, 54, 81 .........

Step-by-step explanation:

ratio of 2nd term and 5th term

$\frac{a {r}^{4} }{a {r} } = \frac{81}{24} \\ {r}^{3} = \frac{81}{24} \\ {r}^{3} = \frac{27}{8} \\ r = \sqrt[3]{ \frac{27}{8} } \\ r = \frac{3}{2} \\ 2nd \: term \: = ar = a \times \frac{3}{2} = 24 \\ a = \frac{24 \times 2}{3} = 16$

a = 16, r = 3/2

1st term = a = 16

2nd term = ar = 16 × 3/2 = 24

3rd term = ar^2 = 16 × 9/4 = 36

4th term = ar^3 = 16 × 27/8 = 54

5th term = ar^4 = 16 × 81/16 = 81

the GP is

16, 24, 36, 54, 81 .........