Question

How many terms are there in an ap whose first term and sixth term is -12and 8. And sum of all 120?

Answer 1

a = -12 & a6 = 8
a + 5d = 8
-12 + 5d = 8
d = 4
sn = 120
n/2 {2a + ( n - 1 ) d } = 120
n ( 2(-12) + ( n - 1 ) ( 4 ) ) = 240
n ( -24 + 4n - 4 ) = 240
4n² - 28n - 240 = 0
n² - 7n - 60 = 0
n² - 12n + 5n - 60 = 0
n(n-12) + 5(n-12) = 0
therefore; we find two value of n
that is;; n = 12 or n = -5