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

Question

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

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Lydia 1 month 2021-08-12T07:43:26+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-12T07:44:53+00:00

    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

    0
    2021-08-12T07:45:20+00:00

    Answer:

    b6sitzdo7f7zkr 7giicyIpu

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