Question

The second term of a gp is 24 and the fifth term is 3 the sum of first 6 numbers is

Answer 1

2nd term gp = 24

ar= 24 .........1eqn..

ar⁴ = 3 .......2nd eqn..

on dividing both eqns..

ar/ar⁴=24/3

1/r³=8

1/8=r³

1/2³= r³

[1/2=r].....3rd eqn

now substitute the value in eqn.1 we get,

ar=24

then, a.1/2= 24

a= 24×2

[a=48]

sum of first 6 terms Sn= a[1-(r)^n]/(1-r)

Sn= 48[1-(1/2)^6]/(1-1/2)

Sn= 48 [1-1/64]/(1/2)

Sn=48[(64-1)/64]/(1/2)

Sn=(48*63/64)/(1/2)

Sn=(48*63*2)/64

Sn=(63*3/2)

Sn=189/2..ans.