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

Answer:

12th term: $a_{12}=5\times 2^{12-1}$

nth term: $a_n=5\times 2^{n-1}$

2nd term: $a_{2}=5\times 2^{2-1}$

4th term: $a_{4}=5\times 2^{4-1}$

(n-1)th term: $a_{n-1}=5\times 2^{n-2}$

6th term: $a_{6}=5\times 2^{6-1}$

Step-by-step 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:

$a_n=5\times 2^{n-1} ...... (1)$

$12^{th}$ term is:

Put n = 12 in (1):

$a_{12}=5\times 2^{12-1}$

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

$a_{2}=5\times 2^{2-1}$

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

$a_{4}=5\times 2^{4-1}$

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

$a_{n-1}=5\times 2^{n-1-1}\\a_{n-1}=5\times 2^{n-2}$

6th term is:  (Put n = 6 in (1))

$a_{6}=5\times 2^{6-1}$