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Can someone please help me with Arithmetic Sequences

Can someone please help me with Arithmetic Sequences-example-1
User Holin
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1 Answer

12 votes

Answer:

287

Explanation:

Sum of A Finite Arithmetic Sequnece is


(a _(1) + a _(n) )/(2) n

Where a1 is first term

an is final term

N is the number of terms.

We know a1 is 1

An is 40 but we don't know n.

To find n, we use the definition of a Arithmetic Sequence


a _(n) = a + (n - 1)d

where d is the common difference. Let use the final term, 40 as a example.

Here the common difference is 3 so we have


40= 1 + (n - 1)3


39 = 3(n - 1)


13 = n - 1


14 = n

So we have 14 terms in this finite series.

Now we compute


(1 + 40 )/(2)(14) = (41)/(2) (14) = 41 * 7 = 287

So the answer is 287

User John Byro
by
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