Question

Consider the arithmetic sequence 13, 24, 35, ....

c. If the nth term is 299, find the value of n.

Answer 1

Answer: 27

Explanation:

The given sequence : 13, 24, 35, ....

Here, first term : a= 13

Common difference: d=24-13 =11

The nth term of arithmetic sequence is given by :-

`a_n=a+(n-1)d`

It is given that the nth term is 299, so put
`a_n=299, a=13 ; d=11`

`299=13+(n-1)11`

Subtract 13 from both sides , we get

`286=(n-1)11`

Divide both sides by 11, we get

`26=n-1`

Add 1 on both sides , we get

`n=27`

Hence, the value of n= 27