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

Arithmetic Progression:
\[\frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots\]

Step 1: Identify the first term \(a\)
\[a = \frac{3}{2}\]

Step 2: Determine the common difference \(d\)
\[d = \frac{1}{2} - \frac{3}{2} = -1\]

Step 3: Apply the \(n\)-th term formula for A.P.
\[a_n = a + (n - 1)d\]

Step 4: Compute the 22nd term
\[a_{22} = \frac{3}{2} + (22 - 1)(-1) = \frac{3}{2} - 21 = \frac{3}{2} - \frac{42}{2} = -\frac{39}{2}\]

Answer:
\[\boxed{-\frac{39}{2}}\]