Question

Find the $n^{\text{th}}$ term of the sequence 2, 5, 10, 17, 26 ...

• A. $n^2$ - 1
• B. $n^2$ + 1
• C. n+2
• D. n+11

Answer 1

The correct option is B $n^2$ + 1

$T_2$ = $T_1$ + 3 = 2 + 3 = $2^2$ + 1 = 5
$T_3$ = $T_2$ + 5 = 5 + 5 = $3^2$ + 1 = 10
$T_4$ = $T_3$ + 7 = 10 + 7 = $4^2$ + 1 = 17
$T_5$ = $T_4$ + 9 = 17 + 9 = $5^2$ + 1 = 26

Similarly $T_n$ = $n^2$ + 1