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Find the first three terms of the arithmetic series. Given a1 = 11, an = 110 and Sn = 726.

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Answer:

The first three terms of the arithmetic series are 11, 20, and 29.

Explanation:

We can use the following formulas to solve this problem:

The nth term of an arithmetic series is given by:
an = a1 + (n - 1)d

The sum of the first n terms of an arithmetic series is given by:
Sn = (n/2)(a1 + an)

where a1 is the first term, an is the nth term, d is the common difference, and Sn is the sum of the first n terms.

We are given a1 = 11 and an = 110, so we can use the first formula to find the common difference d:

an = a1 + (n - 1)d
110 = 11 + (n - 1)d
99 = (n - 1)d

We can also use the second formula to find n:

Sn = (n/2)(a1 + an)
726 = (n/2)(11 + 110)
726 = (n/2)(121)
n = 12

Now that we have found the common difference and n, we can use the first formula again to find the first three terms of the series:

a1 = 11
a2 = a1 + d = 11 + d = 11 + (99/11) = 20
a3 = a2 + d = 20 + d = 20 + (99/11) = 29

Therefore, the first three terms of the arithmetic series are 11, 20, and 29.
User Oskar Dajnowicz
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