Discussion

Explanation:

Given, f(1) = 2

Now,

f(2) = f(1 + 1) = f(1) × f(1) = 2 × 2 = 4 = 22

f(3) = f(1 + 2) = f(1) × f(2) = 2 × 22 = 23

f(3) = f(1 + 3) = f(1) × f(3) = 2 × 23 = 24.   

So, f(n) = 2n

f(a + 1) + f(a + 2) +…+ f(a + n) = 16(2n – 1) 

∴ 2(a + 1) + 2(a + 2) + ... + 2(a + n) = 24(2n – 1) 

∴ 2(a + 1)[1 + 2 + ... 2(n−1)] = 24(2n – 1) 

∴ 2(a + 1)(2n – 1) = 24(2n – 1) 

∴ 2(a + 1) = 24

So, a + 1 = 4

∴ a = 3.

Hence, 3.

» Your doubt will be displayed only after approval.


Doubts


Feedback

Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.


© 2024 | All Rights Reserved | Apti4All