The sum of the 1st 4 terms of an AP is 216 and the sum of the 1st 18 terms is 988. What is the first term.

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The sum of the first n terms of an arithmetic progression with first term a and common difference d is `S_n = (n/2)*(2a + (n - 1)*d)`

Here, S4 = 2*(2a + 3d) = 216 and S18 = 9*(2a + 17d) = 988

=> 2a + 3d = 108 and...

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The sum of the first n terms of an arithmetic progression with first term a and common difference d is `S_n = (n/2)*(2a + (n - 1)*d)`

Here, S4 = 2*(2a + 3d) = 216 and S18 = 9*(2a + 17d) = 988

=> 2a + 3d = 108 and 2a + 17d = 988/9

=> 34a + 51d = 1836 and 6a + 51d = 988/3

Subtract the two equations

=> 34a - 6a = 1836 - 988/3

=> 28a = 4520/3

=> a = 1130/21

The first term of the series is 1130/21

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