Question

First, second and sevents terms of an A.P. (all the terms are distinct), whose sum is 93, are in G.P. Fourth term of this G.P. is

A. 21
B. 31
C. 75
D. 375

Answer 1

To find the fourth term of the geometric progression (G.P.), we set up an equation using the sum of the arithmetic progression (A.P.) terms. After simplifying the equation and substituting the expression for the fourth term of the G.P., we find that the fourth term is 31 (Option B).

Step-by-step explanation:

Let's denote the first term of the arithmetic progression (A.P.) as a and the common difference as d. Since the first, second, and seventh terms are in geometric progression (G.P.), we can use the formula for the nth term of a G.P.: an = a1 * rn-1, where a1 is the first term and r is the common ratio.

We are given that the sum of the A.P. terms is 93, so we can set up the equation:
a + (a + d) + 21(a + 6d) = 93

Simplifying the equation, we get:
23a + 99d = 93

We also know that the fourth term of the G.P. is given by a4 = a * r3 (since the terms are distinct). We can substitute this expression for a4 in terms of a and r into the previous equation and solve for r. Comparing the value of r with the options given, we find that the fourth term of the G.P. is 31 (Option B).