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Arithmetic Progressions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsArithmetic Progressions2 Marks
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.

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