Question

If x, y and z are three consecutive terms of an A.P (where a and d are the first term and common difference respectively). Is the statement given below valid?

$2^x+2^z>2^y$

• A. Yes valid for all values of a and d.
• B. Not valid for all values of a and d
• C. Valid for all values of a and some values of d.
• D. Valid for all values of d and some values of a.

Answer 1

The correct option is A

Yes valid for all values of a and d.

Let a and d be the first term and the common difference of the A.P.

$2^{(a-d)}+2^{(a-d)}>2^a{2}^a(2^d+2^d)>2^a$

Which is true for all a and d.