Find the first five terms of the sequence, defined by

Question:

Find the first five terms of the sequence, defined by

$a_{1}=1, a_{n}=a_{n-1}+3$ for $n \geq 2$

 

Solution:

To Find: First five terms of a given sequence.

Condition: $\mathrm{n} \geq 2$

Given: $a_{1}=1, a_{n}=a_{n-1}+3$ for $n \geq 2$

Put $n=2$ in $n^{\text {th }}$ term $\left(\right.$ i.e. $\left.a_{n}\right)$, we have

$a_{2}=a_{2-1}+3=a_{1}+3=1+3=4\left(\right.$ as $\left.a_{1}=1\right)$

Put $\mathrm{n}=3$ in $\mathrm{n}^{\text {th }}$ term (i.e. $\mathrm{a}_{\mathrm{n}}$ ), we have

$a_{3}=a_{3-1}+3=a_{2}+3=4+3=7\left(\right.$ as $\left.a_{2}=4\right)$

Put $n=4$ in $n^{\text {th }}$ term (i.e. $a_{n}$ ), we have

$a_{4}=a_{4-1}+3=a_{3}+3=7+3=10\left(\right.$ as $\left.a_{3}=7\right)$

Put $n=5$ in $n^{\text {th }}$ term $\left(\right.$ i.e. $\left.a_{n}\right)$, we have

$a_{5}=a_{5-1}+3=a_{4}+3=10+3=13\left(a s a_{2}=10\right)$

First five terms of a given sequence is $1,4,7,10,13$

 

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