Question

Given $f\left(n\right)$ being a real valued function whose domain is the set of positive integers and that $f\left(n\right)$ satisfies the following two properties. $f\left(1\right)=23;f(n+1)=8+3\times f\left(n\right)\text{for}n\ge 1.f\left(n\right)$ takes the form $(a.b^n)-c$ for n=1,2,3,4....and a,b,c are constants. find the sum of $a+b+c$

• A. 16
• B. 20
• C. 17
• D. 31

Answer 1

The correct option is A 16

$f\left(2\right)=8+3f\left(1\right)$

$f\left(3\right)=8+3(8+3f(1\left)\right)$

The following pattern is obtained:

$f\left(n\right)=3^{(n-1)}\times 23+8[1+3+3^2+3^3+....]$

$f\left(n\right)=3^{(n-1)}\times 23+4[3^{(n-1)}-1]$

$f\left(n\right)=27\times 3^{(n-1)}-4$

$f\left(n\right)=9\times 3^n-4$

$a+b+c=9+3+4=16$

Option A is the correct choice