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If 2+4 +6+........ + k = 210, find the value of k.​

User Cheloute
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1 Answer

5 votes

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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User Starko
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