Question

If for a G.P., first term is
${27}^{2}$
and seventh term is
${8}^{2}$
find s8​

Answer 1

Hello !!

Is very simple solve your question. See the resolution below.

Find the common ratio.

r^(n - k) = (An/Ak)

r^(7 - 1) = (64/729)

r^(6) = (64/729)

r = 2/3

Find the sum of the first 8 terms.

Sn = [Ak × r^(n) - k]/(r - k)

S8 = [729 × ((2/3)^(8) - 1)]/(2/3 - 1)

S8 = [729 × (256/6561 - 1)]/(2/3 - 1/1)

S8 = [729 × (-6305/6561)]/((2 - 3)/3)

S8 = [-6305/9]/(-1/3)

S8 = (-6305/9) × (-3/1)

S8 = 18915/9

S8 = 2101.66 approx

Final result : the sum of the first 8 terms is 2101.66 approx.

I hope I have collaborated !