Question

How many terms of AP -6, -11/2,-5 are needed to give the sun -24

Answer 1

Step-by-step explanation:

hello dear ..!!!

there is your answer...!!!!

but it's incomplete because I think given condition is not possible..!!

Hope it's help you..!!!

Answer 2

The number of terms are 20 or 5.

Step-by-step explanation:

To find : How many terms of AP -6, -11/2,-5 are needed to give the sum -24​?

Solution :

The sum formula of an A.P is given by,

$S_n=\frac{n}{2}[2a+(n-1)d]$

Where, the first term is a=-6

The common difference is

$d=-\frac{11}{2}-(-6)$

$d=\frac{-11+12}{2}=\frac{1}{2}$

The sum of n terms is $S_n=-24$

Substitute the values in the formula,

$-24=\frac{n}{2}[2(-6)+(n-1)\frac{1}{2}]$

$-48=n[-12+\frac{n}{2}-\frac{1}{2}]$

$-48=n[\frac{-24+n-1}{2}]$

$-96=(-25+n)n$

$n^2-25n+96=0$

Solve by quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

here, a=1, b=-25 and c=96

$n=\frac{-(-25)\pm\sqrt{(-25)^2-4(1)(96)}}{2(1)}$

$n=\frac{25\pm\sqrt{625-384}}{2}$

$n=\frac{25\pm\sqrt{241}}{2}$

$n=\frac{25+\sqrt{241}}{2},\frac{25-\sqrt{241}}{2}$

$n=20.26,4.7$

The possible value of n which give sum -24 is n=20 and 5.

Therefore, the number of terms are 20 or 5.

#Learn more

In an ap the first term is -5 and last term is 45.if the sum of all numbers in the ap is 120 then how many terms are there and what is the commom differnce

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