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Arithmetic Progressions
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01/06/2021 11:58 am
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The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
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01/06/2021 12:00 pm
Given that,
first term, a = 5
last term, l = 45
Sum of the AP, Sn = 400
Sn = n/2 (a+l)
400 = n/2(5+45)
400 = n/2(50)
Number of terms, n =16
As we know, the last term of AP series can be written as;
l = a+(n −1)d
45 = 5 +(16 −1)d
40 = 15d
Common difference, d = 40/15 = 8/3