An arithmetic series has a common difference of 7. Given that the sum of the first 20 terms of the series is 530, how do you find the first term of the series?

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An arithmetic series has a common difference of 7. Given that the sum of the first 20 terms of the series is 530, how do you find the first term of the series?

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Answer 1 · 2016-03-28T17:42:52

#-5#

Explanation:

With the first term as a and common difference d, the sum for n terms = # na+(n(n-1))/2d#, using 1 + 2 + 3 +..(n-1) = (n-1)(n)/2
Here, n = 20 and d = 7.

20a + ((19)(20)/2)7 = 530

#20a = -100#. So, a = #-5#.

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An arithmetic series has a common difference of 7. Given that the sum of the first 20 terms of the series is 530, how do you find the first term of the series?

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