Question

find the sum of all integers between 84 and 719 which are multiple of 3

Answer 1

Answer:

Sn=  254551 is the required answer.

Step-by-step explanation:

As we have to find the sum of all integers between 84 and 719

So the integers will be :- 85 , 86 , 87 , .... , 718

So let a1 = 85 , a2 = 86 and a3 = 87

a2 - a1 = 86 - 85 = 1

a3 - a2 = 87 - 86 = 1

As , a2-a1 = a3-a2 , so the sequence forms a AP with a = 85 and

d = 86 - 85 = 1 and an = 718

So by the formula , tn = a + ( n - 1 ) d

⇒718 = 85 + ( n - 1 ) 1

⇒718 = 85 + n - 1

⇒718 = 84 + n

⇒n =718 - 84

⇒n = 634

Now as we also know the number of terms n = 634

so by the formula , Sn = $\frac{n}{2} [ 2a + ( n-1 )d ]$

⇒ Sn = $\frac{634}{2} [ 2(85) + (634 - 1 )1$

⇒ Sn = 317 [ 170 + 633 ]

⇒ Sn = 317 [ 803 ]

⇒ Sn=  254551

Answer 2

Answer:

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