Sum of the first two terms of GP is -2 and the fifth term of GP is 4 times the third term of GP, then sixth term of GP is:

Concept:

Geometric Progression (GP): The series of numbers where the ratio of any two consecutive terms is the same, is called a Geometric Progression.

​A Geometric Progression of n terms with first term a and common ratio r is represented as:

a, ar, ar², ar³, ..., ar^n-2, ar^n-1.

Calculation:

Given: Sum of the first two terms of GP is -2 and the fifth term of GP is 4 times the third term of GP

According to the question:

a + ar = -2           ...(1)

ar⁴ = 4 × ar²

r = ±2         ...(2)

Using equation (1), we get:

a = \(-\frac{2}{3}\)

Now, the sixth term of the GP = ar⁵ = \(-\frac{64}{3}\).