Question

How many terms of an AP:......-6,-11/2,-5 are needed to give sum -25? Explain double answer

Answer 1

Answer:

Step-by-step explanation:

-6, -5.5, -5 ........................

a = -6

d= 0.5

n = ?

Sn = -25

Sn = n/2 *(2a +(n-1)d)

-25 = n/2 *(-12 + 0.5n - 0.5)

-50 = n(-12.5 + 0.5n)

-50 = -12.5n +0.5 n^2

-100 = -25n + n^2

0 = n^2 - 25n + 100

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

n = 5 , n = 20

the A. P has some of its terms negative.

So the double answer comes because

sum +ve  and -ve terms get cancelled and the sum including them reamins equal

for ex  6 - 5 = 1,

6 -5 -4 -3 -2-1-0+1+2+3+4 = 1

Answer 2

Answer:

20 (or) 5

Step-by-step explanation:

Given A.P= -6 , -11/2 , -5

therefore,

a=-6

d=-1/2

n=?

we know,  n/2(2a+(n-1)d) = Sum

therefore, n/2<2(-6)+(n-1)1/2>= - 25

*fastforward a few steps *

the equation u get is

n^2 -  25n + 100 = 0

solving the above quadratic equation we get

n = 20 (or) 5