# Math

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Sum of4th and the 6th terms of an a,p is 42 . While the sum of the 3rd and 9th terms of the same a.p is 52. Find the (a) first term (b)common difference (c) sum of the first ten terms of the progression. Solution

• Math -

I assume that "a,p" stands for arithmetic progression. Let the nth term be an.

Since a4 + a6 = 2 a5, a5 = 21.
Since a3 + a9 = 2 a6, a6 = 26

The common difference is
a(n+1) - an = a6 - a5 = 5.

The first term is 1, and the progression is
a1 = 1, a2 = 6, a3 = 11, a4 = 16,
a5 = 21, a6 = 26, a7 = 31, a8 = 36,
a9 = 41, a10 = 46...

The sum of the first 10 terms is
7 + 27 + 47 + 67 + 87 = 235

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