what is the sum of all positive integers lying between 200 and 400 that are multiples of 7
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Answered by
3
The numbers lying between 200 and 400, which are divisible by 7, are
203, 210, 217, … 399
∴First term, a = 203
Last term, l = 399
Common difference, d = 7
Let the number of terms of the A.P. be n.
∴ an = 399 = a + (n –1) d
⇒ 399 = 203 + (n –1) 7
⇒ 7 (n –1) = 196
⇒ n –1 = 28
⇒ n = 29
S=29/2(203+399)=8729
203, 210, 217, … 399
∴First term, a = 203
Last term, l = 399
Common difference, d = 7
Let the number of terms of the A.P. be n.
∴ an = 399 = a + (n –1) d
⇒ 399 = 203 + (n –1) 7
⇒ 7 (n –1) = 196
⇒ n –1 = 28
⇒ n = 29
S=29/2(203+399)=8729
Answered by
2
a = 203
d = 7
L = 399
=> a +(n-1) d = 399
=> 203 + (n-1)7 = 399
=> (n-1) 7 = 196
=> n - 1 = 28
=> n = 29
Sn = n/2 [ a + L]
= 29 / 2 [ 203 + 399]
= 29 × 602 / 2
= 29 × 301
= 8729
d = 7
L = 399
=> a +(n-1) d = 399
=> 203 + (n-1)7 = 399
=> (n-1) 7 = 196
=> n - 1 = 28
=> n = 29
Sn = n/2 [ a + L]
= 29 / 2 [ 203 + 399]
= 29 × 602 / 2
= 29 × 301
= 8729
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