Question

Consider the sequence:

3, 8, 13, 18, 23, ...

Answer 1

`a_n` represents a particular any term and
`a_(n-1)` represents just previous term.

`a_8=38`

Explanation:

In the given recursive formula,

`a_n= a_(n-1)+5`

`a_n` represents
`n^(th) \ term`

and
`a_(n-1)`represents just its previous term.

To find
`a_8`, first five terms are given there. We need to find its previous terms
`a_6 \ and\ a_7`

`a_6 = a_(n-1)+5\\a_6= a_(6-1)+5\\a_6 = a_5 +5\\substitute \ a_5 =23\\a_6 = 23+5=28`

Similarly,

`a_7 = a_(n-1)+5\\a_7= a_(7-1)+5\\a_7 = a_6 +5\\substitute \ a_6 =28\\a_7 = 28+5=33`

Similarly,

`a_8 = a_(8-1)+5\\a_8= a_(8-1)+5\\a_8 = a_7 +5\\substitute \ a_7 =33\\a_8 = 33+5=38`

Thus
`a_8 = 38` is the answer.