Question

Split 64 into three parts such that the numbers are in GP

Answer 1

Hii Nitin,

◆ Answer -

64 = 1 × 4 × 16 = 2 × 4 × 8 = 4 × 4 × 4

● Explaination -

Let a be the first term in GP with common multiple r,

t1 = a

t2 = ar

t3 = ar²

To split 64 into 3 consecutive terms of GP -

64 = t1 × t2 × t3

64 = a × ar × ar²

64 = a^3 × r^3

4^3 = (ar)^3

ar = 4

This question can have several solutions,

(i) When a = 1 & r = 4,

t1 = a = 1

t2 = ar = 4

t3 = ar² = 16

(ii) When a = 2 & r = 2,

t1 = a = 2

t2 = ar = 4

t3 = ar² = 8

(iii) When a = 4 & r = 1,

t1 = a = 4

t2 = ar = 4

t3 = ar² = 4

Thanks dear...