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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.

1 Answer

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Best 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, ..., arn-2, arn-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\(-\frac{64}{3}\).

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