Question

Let the sequence $a_n$ be defined as follows :
$a_{1} = 1, a_{n} = a_{n-1} + 2$ for $n\ge2$.
Write the corresponding series.

• A. $1 + 3+ 5 +7 + 9 + .....$
• B. $1+5 + 9+13 + 17 + ..... $
• C. $1+4 + 7+10+13 +..... $
• D. $1 + 6+11 + 16 + 21 + ..... $

Answer 1

Answer: (A)

We have, $a_{n} = a_{n-1} + 2, n\ge2$ and $a_{1} = 1 $
$\therefore a_{2} = a_{1} +2 = 1 +2 += 3$,
$a_{3}= a_{2} +2 $
$= 3 + 2 = 5$,
$a_{4} = a_{3}+2$
$ = 5 + 2 = 7$,
$ a_{5} = a_{4} +2 $
$= 7 + 2 = 9$.
$\therefore $ The corresponding series is $ 1 + 3 + 5 + 7 + 9 + ...$