TS EAMCET · Maths · Functions
If \(f(1)=3\), and \(f(n+1)-f(n)=3\left(4^n-1\right)\), then \(\forall n \in \mathbf{N}, f(n)=\)
- A \(4^n-1\)
- B \(4^n-5 n+4\)
- C \(4^n-3 n+2\)
- D \(4^n+4 n-5\)
Answer & Solution
Correct Answer
(C) \(4^n-3 n+2\)
Step-by-step Solution
Detailed explanation
We have, \(\quad f(1)=3\) \(\begin{aligned} f(n+1)-f(n) & =3\left(4^n-1\right) \\ f(2)-f(1) & =3(4-1) \\ f(3)-f(2) & =3\left(4^2-1\right) \\ f(n)-f(n-1) & =3\left(4^{n-1}-1\right) \end{aligned}\) Adding, we get…
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