Question

Find the nth term in the following sequence:
10, 19, 34, 55

Answer 1

the nth term is 3n²+7

Answer 2

The nth term of sequence is
`3n^(2)+7`

Explanation:

We need to find out the general recurrence relation of sequence:

`10, 19, 34, 55`

if we see pattern of sequence that every square of each number 'n' is multiple of 3 and addition of 7

check this pattern by
`3n^(2)+7`

For n=1

`3n^(2)+7`

`3(1)^(2)+7`

`3+7`

`10`

For n=2

`3n^(2)+7`

`3(2)^(2)+7`

`3* 4+7`

`12+7`

`19`

For n=3

`3n^(2)+7`

`3(3)^(2)+7`

`3* 9+7`

`27+7`

`34`

And so on..

Therefore, the nth term of sequence is
`3n^(2)+7`