Sum of the first two terms of GP is -2 and the fifth term of GP is 4 t

1.	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:1. \(-\frac{2}{3}\)2. \(-\frac{64}{3}\)3. \(\frac{64}{3}\)4. None of these.
Answer» Correct Answer - Option 2 : \(-\frac{64}{3}\) 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 = \(-\frac{64}{3}\).

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:1. \(-\frac{2}{3}\)2. \(-\frac{64}{3}\)3. \(\frac{64}{3}\)4. None of these.

Answer» Correct Answer - Option 2 : \(-\frac{64}{3}\)

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 = \(-\frac{64}{3}\).

Discussion

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