Question

Write down the nth term of the sequence 5, 8, 13, 20, 29

Answer 1

Hello! To find any number in the arithmetic sequence we can use a formula!

It is given by  $a_n =a_1+(n-1)d$


The geometric sequence formula goes by $S_n = \frac{a_1(1-r^n)}{1-r}$

So for this we notice that there's a start of 5 and is being added 3 to get 8.

and then each time it is added by 2 more to get the next time

5
5+ 3 = 8
8 + 5 = 13
13 + 7 = 20
20 + 9 = 29
29 + 11 = 41
41 + 13 = 54
54 + 15 = 69 
69 + 17 = 83

Your formula is $a_n = (n-1)^2 + 4$
Where n starts at 2 not 1