Question

How many terms of the ap : -6,-11/2,-5,.... Are needed to give the sum -25?

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Given,

Arithmetic Progression = -6, -11/2 , -5, ....

Here we have,

First term (a) = -6

Now,

Common difference :-

d = -11/2 + 6/2

d = 1/2

Also,

S(n) = -25

Using Formula we have,

S(n) = n/2[2a + (n - 1)d]

-25 = n/2[-12 + (n - 1) × 1/2]

-50 = n[-24 + (n - 1)/2]

-100 = n[n - 25]

n² - 25n + 100 = 0

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

n = 20, 5

S(20) = S(5)

Here we get,

Sum of the terms from 5th to 20th is zero