Question

Which term is -401 in the arithmetic sequence -5, -9, -13…?
A. 56th
B. 100th
C. 101st
D. 109th

Answer 1

Well find the common difference of the sequence i.e. d
by subtracting two terms -9 -(-5) = - 4
and first term i.e. a of the sequence is -5

so, plug these in the formula

Term = n/2 ( 2a + (n-1)d)

-401 *2 = n(-10 + (n - 1)-4
=> -802 = n( -10 -4n +4 )
=> -802 = n( -6 - 4n)
=> -802 = -6n - 4n^2
=> 4n^2 + 6n - 802 = 0

solve this quadratic equation.... and you would get two roots... Eliminate the negative root and +ve root would be your answer...

Good luck