Answer:
k = 28
Explanation:
You want to know the last term in an arithmetic series with first term 2, common difference 2, and sum 210.
Sum
The sum of an arithmetic series with n terms is ...
Sn = (2a0 +d(n -1))(n/2)
For a0 = 2 and d = 2, we have ...
210 = (2·2 +2(n -1)(n/2) = (n +1)(n)
(15)(14) = (n +1)(n) ⇒ n = 14 . . . . . . . . . factoring 210
Last term
There are 14 terms in the series. The last one is ...
k = 2n = 2(14) = 28
The value of k is 28.
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