Question

22nd term of the A.P.: \(\frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots\) is

• A. \(\dfrac{45}{2}\)
• B. \(-9\)
• C. \(-\dfrac{39}{2}\)
• D. \(-21\)

Hint:

Use the nth term formula of A.P.: \(a_n = a + (n-1)d\) for direct computation.

Answer 1

The Correct Option is C

This is an A.P. with: \[ a = \dfrac{3}{2}, \quad d = \dfrac{1}{2} - \dfrac{3}{2} = -1 \] Using the formula: \[ a_n = a + (n-1)d = \dfrac{3}{2} + (22 - 1)(-1) = \dfrac{3}{2} - 21 = \dfrac{3 - 42}{2} = -\dfrac{39}{2} \]