Question

What is the sum of a 38–term arithmetic sequence where the first term is 14 and the last term is 154?:)

Answer 1

this one requires a slightly different formula than your last question.

Answer 2

do you know the formula for the sum of a series?

Answer 3

I know a=14 and n=38.
but whats d?

Answer 4

s= n/2(A1+An)

Answer 5

you don't need to calculate d

Answer 6

there are at least two forms for the sum of an arithmetic series...

Answer 7

\[S_n=\frac{n}{2}(2a+(n-1)d)\]and:\[S_n=\frac{n}{2}(a+l)\]where "l" is the last term of the series.

Answer 8

so,
x38=38/2(14+154)?

Answer 9

yes

Answer 10

but not x38 - it is \(S_{38}\)

Answer 11

so is it 3192?:)

Answer 12

if you recall from your previous question, you had:\[x_n=a+(n-1)d\]to get the n'th term

Answer 13

yes

Answer 14

3192

Answer 15

so if you look at the first equation for the sum of a series we can see:\[S_n=\frac{n}{2}(2a+(n-1)d)\]\[\qquad=\frac{n}{2}(a+a+(n-1)d))\]\[\qquad=\frac{n}{2}(a+x_n)\]

Answer 16

that is how the second form of the sum is derived.

Answer 17

hope that makes sense?