Question

The sum of the first two terms of a Geometric Progression is 36 and the product of the first and third terms is 9 times the second term. Find the sum of the first 8 terms.

Answer 1

Step-by-step explanation:

a+ar=36

a(ar2)=9ar

ar=9

a=27

r=1/3

sum of first eight terms

27((1-(1/3)7)/1-1/3

27(1-1/2187)/2/3

3×27(2186/2187)/2

1093/243

Answer 2

Step-by-step explanation:

a+ar=36..... 1

a.ar^2=9ar......2

taking equation nor 2

a.ar^2=9ar

a.ar^2/ar=9

a and r get cancel and ar remains

therefore ar=9........3

taking equ 2

a+ar=36

putting ar =9

a+9=36

a=36-9

a=27

by taking equation nor3

ar=9

27r=9

r=9/27

r=1/3

by taking sn formula

sn=a(1-r^n)/1-r

= 27(1-1/3)^7/1-1/3

= 27(3-1/3)^7/2/3

=27×3(3^7-1/3^7)/2/3

=27(2187-1/2187)×3/2

=27×3(2186/2187)/2

=by solving this we have

=1093/243

thank u