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

The Correct Option is B

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): \(22\)