-  The 32nd term is 127

The given series is an arithmetic progression with the first term, a = 3 and common difference, d = 4. We need to find the 32nd term of the series.

The formula to find the nth term of an arithmetic progression is given by:

an = a + (n - 1) d

where,

an is the nth term of the AP

a is the first term of the AP

d is the common difference

n is the position of the term to be found

Substituting the given values in the formula, we get:

a32 = 3 + (32 - 1) 4

a32 = 3 + 31 x 4

a32 = 3 + 124

a32 = 127

Therefore, the 32nd term of the given series is 127, which is Option D.

To summarize the solution:

• The given series is an arithmetic progression with a = 3 and d = 4.
• The formula to find the nth term of an AP is an = a + (n - 1) d.
• Substituting the given values in the formula, we get a32 = 3 + (32 - 1) 4.
• Solving the expression, we get a32 = 127.
• Hence, the correct answer is Option D.