How many terms of the A.P. 22+26+30+… has the sum 400?

Options

A. 9
B. 10
C. 11
D. None of these

Answer

B

Explanation

Here a=22, d=26-22=30-26=4
`"Let "S_(n)=400`
`rArr " "(n)/(2)[2a+(n-1)d]=400`
`rArr " "(n)/(2)[2xx22+(n-1)xx4]=400`
`rArr " "n^(2)+10n-200=0`
`rArr " "(n+20)(n-10)=0`
`rArr " "n+20=0 or n-10=0`
`rArr " "n=-20 or n=10`
But the number of terms cannot be negative.
`therefore" "n=10`