Question

Find the sum of the first 24 terms of the arithmetic progression (AP) whose nth term is given by (a_n = 3 + 2/3n).

a) 576

b) 600

c) 624

d) 648

Answer 1

To find the sum of the first 24 terms of the given arithmetic progression, we can use the formula for the sum of an arithmetic series, which is Sn = n/2(a1 + an). Plugging in the values and simplifying, the sum is equal to 228.

Step-by-step explanation:

To find the sum of the first 24 terms of the arithmetic progression (AP) with the nth term given by a_n = 3 + \frac{2}{3}n, we can use the formula for the sum of an arithmetic series.

The formula for the sum of an arithmetic series is S_n = \frac{n}{2}(a_1 + a_n).

Plugging in the given values, we have S_{24} = \frac{24}{2}(3 + \frac{2}{3} \cdot 24).

Simplifying the expression, we get S_{24} = 12(3 + 16) which equals 12(19) and the sum is equal to 228.