sequence of black balls and white balls.

Question

Following is a sequence of black balls and white balls. How many black balls are needed for the 100th term?

Answer 1

The 1st picture (picture #1) has 2•1 or 2 black circles and one white circle.

The 2nd picture (picture #2) has 2•2 or 4 black circles and one white circle.

The 3rd picture (picture #3) has 2•3 or 6 black circles and one white circle.

The 100th picture (picture #100) will have 2•100 or 200 black circles and one white circle.

Answer 2

This is an arithmetic sequence where the initial value is 2 (black balls), and there is an increase of 2 black balls with every term.

equation for nth term of arithmetic sequence:

a(n) = a(1) + (n-1)*d

here n = 100, a(1) = 2 and d = 2 so

a(100) = 2 + 99(2) = 200