Find the 10 th term of the following geometric sequence. 5, 15, 45, 135, ...

T10 = 98415

Step-by-step explanation:

The nth term of a GP series is Tn = ar^ (n-1), where a = first term and r = common ratio. The general form of a GP is a, ar, ar^2, ar^3 and so on

T10 = ar^ (10-1) = ar^9

here,

first term, a = 5

Common ratio, r determines how the next term varies in accordance with previous term

Getting the common ratio is by saying that

second term / first term = third term / second term

15 / 5 = 45 / 15

3 = 3

=> r = 3

Putting the values of a = 5, r=3 in the formula T10 = ar^9

=> T10 = (5) (3) ^9 (There was first of all problem of multiplication here)

= 5*19683

T10 = 98415

The answer is 98,415

Step-by-step explanation:

This is because the pattern is to multiply by 3, when you keep on multiplying the term by 3 to get the next term until you get to the 10th term, the answer is 98,415.