Question

How many terms of he ap -6, -5.5, -5 are needed to give the sum -25? Explain double answer?

Answer 1

The AP given is-

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

Now, we have

sum=-25

a=-6

d=0.5

n=?

the required formula for the given question will be the formula to find the sum of n terms in an automatic progression, which is as follows-

Sum = n/2 {2a + (n-1)d }

-25 = n/2 {2*-6 + (n-1)0.5}

-25 = n/2 {-12+ 0.5n -0.5}

-25 = -12.5n/2 + 0.5n^2/2

on solving the above equation,

we get

n= 5

Answer 2

a = - 6

d = - 6 + 5.5 = 0.5

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

$\small - 25 = \frac{n}{2} (2 \times - 6 + (n - 1) 0.5$

$\small - 50 = n( - 12 + 0.5n - 0.5)$

$- 50 = - 12.5n + 0.5 {n}^{2}$

$0.5 {n}^{2} - 12.5n + 50 = 0$

On solving we get

n = 5, 20

Hope it helps ✌️ ✌️