Question

1) The first term of an arithmetic sequence is 6
and the common difference is 4. How
many
terms of this sequence, starting from the first,
are to be added to get 510?​

Answer 1

Answer:

let the series has n terms

n/2{2.6+(n-1).4}=510

n/2{12+4n-4}=510

n/2(8+4n)=510

n/2.4(2+n)=510

2n(2+n)=510

n(2+n)=510/2=255

n^2+2n-255=0

n^2+17n-15n-255=0

n(n+17)-15(n+17)=0

(n+17)(n-15)=0

n-15=0 , n=15

n+17=0, n is not negative

so the number of terms is 15