Explain the terms in the formula sn= n/2 2a+(n-1)d
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The sum of nth terms of an AP with first term a and common difference d is Sn=n2(2a+(n-1)d) The sum of first 6 terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1:3.
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In the given formula,
Sn = Sum of n terms
n = Total number of terms
a = The first term
d = common difference
1. The given formula is . It is used to find the sum of n terms in an arithmetic progression.
2. For example, A.P. = 2,4,6,8,10,12
n = 6, a = 2,
d = 6-4 = 2 (The difference between two consecutive terms)
Therefore, the sum of 6 terms will be
Hence, the sum of 6 terms is equal to 42.
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