Question

Can someone please help me with Arithmetic Sequences

Answer 1

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