Sequences And Series

This is a geometric series where the first term

a%20%3D%202

and the common ratio

r%20%3D%203

.
The sum of the first

n

terms of a geometric series is given by the formula:

S_n%20%3D%20%5Cfrac%7Ba(r%5En%20-%201)%7D%7Br%20-%201%7D

To find the sum, we need to first determine the number of terms in the series.
Given the last term

T_n%20%3D%204374

, we can find

n

using the formula:

T_n%20%3D%20a%20r%5E%7Bn-1%7D%20%5Cquad%20%5CRightarrow%20%5Cquad%204374%20%3D%202%20%5Ctimes%203%5E%7Bn-1%7D

Solving for

n

, we get

n%20%3D%209

.
Now, we can calculate the sum of the first 9 terms:

S_9%20%3D%20%5Cfrac%7B2(3%5E9%20-%201)%7D%7B3%20-%201%7D%20%3D%206560

Chapter Questions
1 MCQs