Question

how many terms of the airthmetic sequence -3,2,7 must be added together for the sum of the series to be 116​

Answer 1

-3,2,7,....

a= -3 , d= 2-(-3) = 5

Sn =116

Sn =n/2[a+an]

Sn= n/2[a+a+(n-1)d]=116

n/2[2*(-3)+(n-1)5] =116

n[-6+5n-5] = 232

5n² -11n -232 = 0

5n² - 40n+29n -232=0

5n(n-8)+29(n-8)=0

(n-8)(5n+29) = 0

n =8 or n=-29/5

number of terms can't be in fraction so we take, n =8

hence 8 terms should be added together to get sum 116