Question

Find the sum of first 8 terms of a geometric series whose fourth term is 81 and common ratio is 3

Answer 1

hope it helps.... please mark brainliest

Answer 2

Answer:

9840

Step-by-step explanation:

∴ General Form of a geometric sequence with first term a is a,ar,ar²...arⁿ⁻¹.

Given that Fourth term is 81.

The fourth term of the geometric series = ar³ = 81

Given that the common ratio r =  3.

⇒ ar³ = 81

⇒ a(3)³ = 81

⇒ a(27) = 81

⇒ a = 81/27

⇒ a = 3

Hence, a = 3, r = 3.

Now,

∴ Sum of n terms of GP Sn = a(1 - rⁿ)/(1 - r)

Sum of first 8 terms = S₈

= 3(1 - 3⁸)/(1 - 3)

= 3(-6560)/(-2)

= 19680/2

= 9840.

Therefore, Sum of first 8 terms of a Geometric Series is 9840.

Hope this helps!