Let the sequence an be defined as follows: a1 = 1, an = an-1 + 2 for n ge2. Write the corresponding series.

Question

Let the sequence an be defined as follows: a1 = 1, an = an-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 + .....

Tardigrade Admin · Accepted Answer

We have, an = an-1 + 2, n ge2 and a1 = 1 ∴ a2 = a1 +2 = 1 +2 += 3, a3= a2 +2 = 3 + 2 = 5, a4 = a3+2 = 5 + 2 = 7, a5 = a4 +2 = 7 + 2 = 9. ∴ The corresponding series is 1 + 3 + 5 + 7 + 9 + ...

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

$1 + 3 + 5 + 7 + 9 + .....$

$1 + 5 + 9 + 13 + 17 + .....$

$1 + 4 + 7 + 10 + 13 + .....$

$1 + 6 + 11 + 16 + 21 + .....$

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

Q. Let the sequence an​ be defined as follows : a1​=1,an​=an−1​+2 for n≥2. Write the corresponding series.

1+3+5+7+9+.....

1+5+9+13+17+.....

1+4+7+10+13+.....

1+6+11+16+21+.....