Question
Write the first five terms in the following sequences:$\text{a}_1=1,\text{a}_\text{n}=\text{a}_{\text{n}-1}+2,\text{n}>1$
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Answer
$\text{a}_1=1,\text{a}_\text{n}=\text{a}_{\text{n}-1}+2,\text{n}\geq2$
$\text{a}_2=\text{a}_{\text{2}-1}+2=\text{a}_{1+2}=3$ $[\because\text{a}_1=1]$
$\text{a}_3=\text{a}_{\text{3}-1}+2=\text{a}_{2}+2=5$ $[\because\text{a}_2=3]$
$\text{a}_4=\text{a}_{\text{4}-1}+2=\text{a}_{3}+2=7$ $[\because\text{a}_3=5]$
$\text{a}_5=\text{a}_{\text{5}-1}+2=\text{a}_{4}+2=9$ $[\because\text{a}_4=7]$
$\therefore$ The first 5 terms os series are 1, 3, 5, 7, 11.
$\text{a}_2=\text{a}_{\text{2}-1}+2=\text{a}_{1+2}=3$ $[\because\text{a}_1=1]$
$\text{a}_3=\text{a}_{\text{3}-1}+2=\text{a}_{2}+2=5$ $[\because\text{a}_2=3]$
$\text{a}_4=\text{a}_{\text{4}-1}+2=\text{a}_{3}+2=7$ $[\because\text{a}_3=5]$
$\text{a}_5=\text{a}_{\text{5}-1}+2=\text{a}_{4}+2=9$ $[\because\text{a}_4=7]$
$\therefore$ The first 5 terms os series are 1, 3, 5, 7, 11.
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