Question

Match the terms of this geometric sequence with their term numbers. 5, 10, 20, 40, 80, 160, ...

Boxes: [12th term] [nth term] [2nd term] [4th term] [(n-1)th term] [6th term]
Terms to be put in boxes: 5*2^4-1, 5*2^2-1, 5*2^12-1, 5*2^n-2, 5*2^6-1

Answer 1

12th term:
`a_(12)=5* 2^(12-1)`

nth term:
`a_n=5* 2^(n-1)`

2nd term:
`a_(2)=5* 2^(2-1)`

4th term:
`a_(4)=5* 2^(4-1)`

(n-1)th term:
`a_(n-1)=5* 2^(n-2)`

6th term:
`a_(6)=5* 2^(6-1)`

Explanation:

The first term of GP, a = 5

Common ratio, r = 2

Formula for
`n^(th)` term of a GP,
`a_n=ar^(n-1)`.

Putting the values of a and r. So,
`n^(th)` term is:

`a_n=5* 2^(n-1) ...... (1)`

`12^(th)` term is:

Put n = 12 in (1):

`a_(12)=5* 2^(12-1)`

2nd term is : (Put n = 2 in (1))

`a_(2)=5* 2^(2-1)`

4th term is: (Put n = 4 in (1))

`a_(4)=5* 2^(4-1)`

(n-1)th term is, put value of n as (n-1) in equation 1:

`a_(n-1)=5* 2^(n-1-1)\\a_(n-1)=5* 2^(n-2)`

6th term is: (Put n = 6 in (1))

`a_(6)=5* 2^(6-1)`