Question

How many terms of AP -6, -11/2,-5 are needed to give the sun -25

Answer 1

Step-by-step explanation:

Given:

1. AP is -6, -11/2,-5.
2. Sn = -25.

To find: n=?

In A.P:

a= -6.

d = A2 - a

=> -11/2-(-6)

=> -11/2+6

=> -11+12/2

=> ½.

Formula of sum of n Integers:

$sn = \frac{n}{2} \times (2 \times a \: + (n - 1) \times d)$

=> -25 = n/2×(2×(-6)+(n-1)×(⅓))

=> -25 = n/2×(-12+½n-½)

=> -25 = n/2×(-24+n-1/2)

=> -25 = n/2×(-25+n/2)

=> -25 = -25n+n²/4

=> -25×4 = -25n+ n²

=> -100=-25n+n²

=> n²-25n+100=0

By factorising the equation:

n²-25n+100=0

n²-20n-5n+100=0

n(n-20)-5(n-20)=0

(n-20)×(n-5)=0

n=20 or 5.