Let sequence a_{n} be defined as follows: {a₁} = 1,{aₙ} = {a_{n - 1}} + 2 for n, ge ,2 Fin

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8. Sequences and Series

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Let the sequence $a_{n}$ be defined as follows:

${a_1} = 1,{a_n} = {a_{n - 1}} + 2$ for $n\, \ge \,2$

Find first five terms and write corresponding series.

A

$1+3+5+7+9+\ldots$

B

$1+3+5+7+9+\ldots$

C

$1+3+5+7+9+\ldots$

D

$1+3+5+7+9+\ldots$

Solution

We have

$a_{1}=1, a_{2}=a_{1}+2=1+2=3, a_{3}=a_{2}+2=3+2=5$

$a_{4}=a_{3}+2=5+2=7, a_{5}=a_{4}+2=7+2=9$

Hence, the first five terms of the sequence are $1,3,5,7$ and $9 .$ The corresponding series is $1+3+5+7+9+\ldots$

Standard 11

Mathematics

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