Question

For what values of the parameter ‘a’ are there real values of x such that 5^{1 + x} + 5^{1 – x}, $\frac{a}{2}$, 25^x + 25^–x are three consecutive terms of an A.P. –

• A. a < 12
• B. a < –12
• C. a ³ 12
• D. None of these

Answer 1

Answer: (C)

a ³ 12

Answer 2

2$\left( \frac{a}{2} \right)$ = (5^{1 + x} + 5^{1 – x}) + (25^x + 25^–x)

̃ a = 5 (5^x + 5^–x) + (5^2x + 5^–2x)

= 5 {(5^x/2 – 5^–x/2)² + 2.5^x/2 . 5^–x/2} + {(5^x – 5^–x)² + 2 . 5^x . 5^–x}

= 5 {(5^x/2 – 5^–x/2)² + 2} + (5^x – 5^–x)² + 2 a ³ 5 × 2 + 2 a ³ 12.