Question

In the following questions, two statements (i) and (ii) are given. Choose the valid statement.

1. The 6^th term of the progression 2, 6, 18, ... is 162.
2. Sum of n terms of GP = `(a(1 - r^n))/(1 - r)`.

विकल्प

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

(i) a = 2

r = `6/2`

= 3

n^th term = `a.r^(n - 1)`

4^th term = 18 × 3

= 54

5^th term = 54 × 3

= 162

6^th term = 162 × 3

= 486

Since 162 is the 5^th term, not the 6^th, the statement is false.

(ii) 

This statement is Correct. This is the standard, mathematically valid formula for calculating the sum (S_n) of the first n terms of a Geometric Progression where r ≠ 1. While it is most commonly used when r < 1 to avoid negative numbers in the fraction, it works for any value of r (except 1).