Question

If a$_1$ = 4 and $a_{n+1}=a_{n}+4n\quad for\quad n\ge1.$ then the value of a$_{100}$ is

• A. 19804
• B. 18904
• C. 18894
• D. 19904

Answer 1

Answer: (A)

19804

Answer 2

The correct answer is A:19804
Given that: $a_1=4, a_{n+1}=a_n+4n ,$
$\therefore$ for $n=1=a_2-a_1=4\times1$ $\therefore [a_{n+1}-a_n=4n]$
for $n=2=a_3-a_2=4\times2$
$\therefore$ for $n=99=a_{100}-a_{99}=4\times99$
So, we get
$a_{100}-a_1=4 (1+2+.....+99)$(on adding)
⇒$a_{100}=4+4\times\frac{99(99+1)}{2}$
⇒$a_{100}=19804$