Question:medium
Let \( f:\mathbb{N}\to\mathbb{N} \) be such that \( f(1)=2 \) and \( f(x+y)=f(x)f(y) \). If \( \sum_{k=1}^{n} f(a+k)=16(2^n-1) \), then \( a \) is
Let \( f:\mathbb{N}\to\mathbb{N} \) be such that \( f(1)=2 \) and \( f(x+y)=f(x)f(y) \). If \( \sum_{k=1}^{n} f(a+k)=16(2^n-1) \), then \( a \) is
Show Hint
Functional equations like \( f(x+y)=f(x)f(y) \) usually give exponential functions.
Updated On: May 1, 2026
- \( 3 \)
- \( 4 \)
- \( 5 \)
- \( 6 \)
- \( 7 \)
Show Solution
The Correct Option is B
Solution and Explanation
Was this answer helpful?
0
Top Questions on sequences
- 10, 30, 68, 130, ___ ,350
find the missing number?- JEE Main - 2024
- Mathematics
- sequences
Find the missing value in the logic/series figure provided in the question.
- JEE Main - 2021
- Mathematics
- sequences
- Let be a sequence such that a1+a2+....+ an=\(\frac{n^2+3n}{ (n+1 ) (n+2)}\). If \(28∑^{10}_{k=1}\frac{1}{a_k} =\) P1P2P3 . . . Pm , where p1, p2, …..pm are the first m prime numbers, then m is equal to
- JEE Main - 2023
- Mathematics
- sequences
If aa is the greatest term in the sequence \(a_n=\frac{n^3}{n^4+147},n=1,2,3,...,\) then a is equal to______________.
- JEE Main - 2023
- Mathematics
- sequences
- Want to practice more? Try solving extra ecology questions todayView All Questions
