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.