Answer:
The nth term of sequence is [tex]3n^{2}+7[/tex]
Step-by-step explanation:
We need to find out the general recurrence relation of sequence:
[tex]10, 19, 34, 55[/tex]
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 [tex]3n^{2}+7[/tex]
For n=1
[tex]3n^{2}+7[/tex]
[tex]3(1)^{2}+7[/tex]
[tex]3+7[/tex]
[tex]10[/tex]
For n=2
[tex]3n^{2}+7[/tex]
[tex]3(2)^{2}+7[/tex]
[tex]3\times 4+7[/tex]
[tex]12+7[/tex]
[tex]19[/tex]
For n=3
[tex]3n^{2}+7[/tex]
[tex]3(3)^{2}+7[/tex]
[tex]3\times 9+7[/tex]
[tex]27+7[/tex]
[tex]34[/tex]
And so on..
Therefore, the nth term of sequence is [tex]3n^{2}+7[/tex]
