Question

(a) (b)
5 3 (d) 6
7. How many terms of an AP must be taken for their sum to be equal to 120 if its third term is 9 and
the difference between the seventh and second term is 20 ?
(a) 7 (b) 8 (c) 9 (d) 6

Answer 1

Hope it helps you...▶️▶️

Answer 2

8 terms of an AP must be taken for their sum to be equal to 120

Step-by-step explanation:

Formula of nth term in AP :

$a_n=a+(n-1)d$

Substitute n = 3

$a_3=a+(3-1)d$

$a_3=a+2d$

We are given that third term is 9

So.a+2d=9 --- A

Substitute n = 7

$a_7=a+6d$

Substitute n = 2

$a_2=a+d$

We are given that the difference between the seventh and second term is 20

$a+6d-(a+d)=20\\a+6d-a-d=20\\5d=20\\d = 4$

Substitute the value of d in A

a+2(4)=9

a+8=9

a=1

Formula of sum of first n terms :

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

We are given that sum is 120

Substitute the values

$120=\frac{n}{2}(2(1)+(n-1)(4))\\240=n(2+4n-4)\\240=n(4n-2)\\240=4n^2-2n\\120=2n^2-n\\2n^2-n-120=0\\(n-8)(2n+15)=0\\n=8,\frac{-15}{2}$

Since number of terms should be a whole number .

So, 8 terms of an AP must be taken for their sum to be equal to 120

#Learn more:

How many terms of an AP must be taken for their sum to be equal to 120 if its third term is 9 and

the difference between the seventh and second term is 20 ?

(a) 7 (b) 8 (C) 9 (d) 6

https://brainly.in/question/13108995