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What will be the seventh number in the following series of geometric progression series?

5, 35, 245, 1715, _____


1. 84035
2. 4117715
3. 12005
4. 588245

1 Answer

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Best answer
Correct Answer - Option 4 : 588245

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.

  • The sum of the first n terms of a GP is:

    Sn = \(\rm a\left(\frac{r^n\ -\ 1}{r\ -\ 1}\right)\).

  • nth  term of the G.P. is an = arn−1

Calculation:

For the given geometric series 5, 35, 245, 1715, __ we have a = 15 and r = 7.

nth  term of the G.P. is an = arn−1

⇒ a7 = 5 × 7(7 - 1)

⇒ a7 = 5 × 76

⇒ a7 = 588245

Hence, "588245" is the correct answer.

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