Question

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

Answer 1

Answer:

The nth term of sequence is $3n^{2}+7$

Step-by-step 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

$3n^{2}+7$

$3(2)^{2}+7$

$3\times 4+7$

$12+7$

$19$

For n=3

$3n^{2}+7$

$3(3)^{2}+7$

$3\times 9+7$

$27+7$

$34$

And so on..

Therefore, the nth term of sequence is $3n^{2}+7$

Answer 2

The nth term is 3n²+7