Question

Consider the sequence: 3, 8, 13, 18, 23, ...

Answer 1

Answer:

$a_n$ represents a particular any term and $a_{n-1}$ represents just previous term.

$a_8=38$

Step-by-step 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.