Question

Assume that $f\left(1\right)=0$ and that for all integers m and n. $f(m+n)=f\left(n\right)+3(4mn-1)$ then f(19)=

• A. 213
• B. 209
• C. 194
• D. 199

Answer 1

The correct option is A 213

Given $f(m+n)=f\left(n\right)+3(4mn-1),f\left(1\right)=0$

Put $n=1⟹f(m+1)=f\left(1\right)+3(4m-1)=12m-3$

Let $m=18$

$⟹f(18+1)=12\times 18-3=216-3=213$