Question

Write a recursive formula for the sequence 7, 13, 19, 25, 31… then find the next term.

Answer 1

Given:

Sequence 7, 13,19, 25, 31........

Find-:

The next term

Explanation-:

First-term = 7

Let

`a_n=a_(n-1)+6`

Because sequence value increases the net term should be added.

So,

`\begin{gathered} a_n=a_(n-1)+6 \\ \\ a_2=a_(2-1)+6 \\ \\ a_2=a_1+6 \\ \\ a_2=7+6 \\ \\ a_2=13 \end{gathered}`

For the next value n is 6.

So,

`\begin{gathered} a_n=a_(n-1)+6 \\ \\ a_6=a_(6-1)+6 \\ \\ a_6=a_5+6 \\ \\ a_6=31+6 \\ \\ a_6=37 \end{gathered}`

So,

`a_n=a_(n-1)+6,\text{ where}a_1=7;37`