Question

How many terms are added in 24+20+16+ ....... 10 make the sum 72?

Answer 1

Hey mate !!

Here's your answer !!

As given above we can clearly see that the given series forms an AP. So we can use the sum formula to calculate it.

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

So the values are :

a = 24

d = -4

n = ?

Sn = 72

So substitute in the formula to get the answer:

= 72 = n / 2 [ 2 ( 24 ) + ( n - 1 ) -4 ]

= 72 = n / 2 [ 48 - 4n + 4 ]

= 72 * 2 = n [ 52 - 4n ]

= 144 = 52n - 4n²

= 4n² - 52n + 144 = 0 ------ Dividing by 4 throughout the equation we get,

= n² - 13n + 36

Factorizing the above quadratic equation we get,

= n² - 9n - 4n + 36 = 0

= n ( n - 9 ) -4 ( n - 9 ) = 0

= ( n - 4 ) ( n - 9 ) = 0

= n = 4 , 9

So the number of terms can be both 4 terms and 9 terms. This is because since the AP is decreasing. 

Hope it helps !!

Cheer !! 

Answer 2

Answer:

4 terms and 9 terms.

Step-by-step explanation:

Given A.P is 24,20,16,...

so, the first term, a=24

the common difference, d=20−24

=−4.

The sum of first n terms of A.P is given by

2 n  [2a+(n−1)d]=  2 n

​ [48−(n−1)4]

Given, the sum is 72.

so,  

2 n [48−(n−1)4]=72

⇒24n−n(n−1)2=72

⇒2n  2 −26n+72=0⇒n  2  −13n+36=0

⇒n=4 or 9.

∴ 4 terms and 9 terms add upto 72.