Question

If the fourth term of a series in geometric progression is 24 and the seventh term is 192 find the sum of its first ten terms

Answer 1

Step-by-step explanation:

Let a be first term of GP

and r be common ratio

then nth term is given by a*r^n-1

4th term

a*r^3=24

7th term

a*r^6=192

divide both eqn

we will get

a*r^6/a*r^3 =192/24

r^3=8

r=2

a*2^3=24

a*8=24

a=3

sum of n terms = a*(r^n-1)/r-1

=3*(2^10-1)/1

=3*1024=3072