Question

Q7

In an AP, the first term is -12 and the last term is 40. If the sum of all terms is 196, find the
common difference and number of terms.
​

Answer 1

Answer: d = 4, n = 14

Explanation:

`S_n=(a_1+a_n)/(2)\cdot n`

`\text{Given:}\quad S_n=196, a_1=-12, a_n=40\\\\\\196=(-12+40)/(2)\cdot n\\\\392=28n\\\\14=n`

`a_(n)=a_1+d(n-1)\\a_(14)=a_1+d(14-1)\\40=-12+d(14-1)\\52 = 13d\\4=d`