The 4th term of a G.P. is square of its second term, and the first term is – 3.Determine its 7th term.

Sure, let's solve the problem step by step.

Given:

• The first term of the geometric progression (G.P.) is -3.
• The 4th term of the G.P. is the square of its second term.

Step 1: Find the common ratio (r) To find the common ratio (r), we can use the formula for the nth term of a G.P., which is given by: an = a1 * r^(n-1)

Since the 4th term is the square of the second term, we can write: a4 = (a1 * r^(4-1))^2

Substituting the given values, we have: (-3 * r^3)^2 = 9 * r^6

Simplifying, we get: 9 * r^6 = 9 * r^6

This equation is true for any value of r. Therefore, we cannot determine the exact value of the common ratio.

Step 2: Find the 7th term (a7) To find the 7th term (a7), we can use the formula for the nth term of a G.P.: an = a1 * r^(n-1)

Substituting the given values, we have: a7 = -3 * r^(7-1)

Since we cannot determine the exact value of r, we cannot determine the exact value of the 7th term (a7).