Find the sum of all multiple of 7 between 100 and 300
4 answers
whats ur answer?
In this interval:
The first number divisible by 7 is 105
The last number divisile by 7 is 294
Each number is a term of AP:
an = a1 + ( n - 1) d
where
a1 = 105
an = 294
d = 7
an = 294 = 105 + ( n - 1) d =
105 + ( n - 1) ∙ 7 = 105 + 7 n - 7 = 98 + 7 n
294 = 98 + 7 n
294 - 98 = 7 n
196 = 7 n
n = 196 / 7 = 28
Sn is the sum of n terms in the arithmetic progression:
Sn = ( n / 2 ) ( a1 + an )
In tis case:
n = 28
Sn = S28
Sn = ( n / 2 ) ( a1 + an )
Sn = S28 = ( 28 / 2 ) ( 105 + 294 )
Sn = 14 ∙ 399
Sn = 5 586
The first number divisible by 7 is 105
The last number divisile by 7 is 294
Each number is a term of AP:
an = a1 + ( n - 1) d
where
a1 = 105
an = 294
d = 7
an = 294 = 105 + ( n - 1) d =
105 + ( n - 1) ∙ 7 = 105 + 7 n - 7 = 98 + 7 n
294 = 98 + 7 n
294 - 98 = 7 n
196 = 7 n
n = 196 / 7 = 28
Sn is the sum of n terms in the arithmetic progression:
Sn = ( n / 2 ) ( a1 + an )
In tis case:
n = 28
Sn = S28
Sn = ( n / 2 ) ( a1 + an )
Sn = S28 = ( 28 / 2 ) ( 105 + 294 )
Sn = 14 ∙ 399
Sn = 5 586
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Thank you big time
2 answers