Question

Choose the correct choice in the following and justify : $11^{th}$ term of the AP: $– 3, -\frac 12, 2,.....$ is

• A. 28
• B. 22
• C. -38
• D. -48$\frac 12$

Answer 1

Answer: (B)

22

Answer 2

Given that,
A.P. $-3, -\frac 12, 2, .......$
First term $a = −3$
Common difference, $d = a_2 − a_1$
$d = -\frac 12 - (-3)$

$d = -\frac 12 + 3$

$d = \frac {-1+6}{2}$

$d = \frac 52$
We know,
$a_n = a + (n-1)d$

$a_{11} = -3 + (11-1)(\frac 52)$

$a_{11} = -3 + 10 \times \frac 52$
$a_{11} = -3 + 25$
$a_{11}= 22$

Hence, the correct option is (B): $22$