Question

Find the oth term of the geometric sequence 7, 14, 28, ...

Answer 1

The nth term of the geometric sequence 7, 14, 28, ... is:

`a_n=7\cdot \:2^(n-1)`

Explanation:

Given the geometric sequence

7, 14, 28, ...

We know that a geometric sequence has a constant ratio 'r' and is defined by

`a_n=a_1\cdot r^(n-1)`

where a₁ is the first term and r is the common ratio

Computing the ratios of all the adjacent terms

`(14)/(7)=2,\:\quad (28)/(14)=2`

The ratio of all the adjacent terms is the same and equal to

`r=2`

now substituting r = 2 and a₁ = 7 in the nth term

`a_n=a_1\cdot r^(n-1)`

`a_n=7\cdot \:2^(n-1)`

Therefore, the nth term of the geometric sequence 7, 14, 28, ... is:

`a_n=7\cdot \:2^(n-1)`