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Question
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
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Solution
In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,
`S_n =n/2 [2a + (n -1)d]`
Where a = first term for the given A.P.
d = common difference of the given A.P
n = number of terms
50, 46, 42, ... to 10 terms
Common difference of the A.P. (d)
`= a_2 - a_1`
= 46 - 50
= -4
Number of terms (n) = 10
First term for the given A.P. (a) = 50
So using the formula we get
`S_10 = 10/2 [2(50) + (10 - 1)(-4)]`
= (5)[100 + (9)(-4)]
= (5)[100 - 36]
= (5)[64]
= 320
Therefore the sum of first 10 terms for the given A.P is 320
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