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

Given A.P.:
\[ \frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots \]

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

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

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

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

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