# Math Help - Arithmetic Series

1. ## Arithmetic Series

In an arithmetic series, the terms of the series are equally spread out. For example, in
1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic series is
3, the last term is 136, and the sum is 1,390, what are the first 3 terms?

Did I do this right?

$sn=n/2(a1+an)$

$1390=n(139)/2$

$n=20$

$increment = (136-3)/(n-1)$

$133/(20-1)$

$133/19 = 7$

So it'd be $3+10+17...136 = 1390.$

2. yes, your final series is correct

3. Hello, A Beautiful Mind!

If the first term in an arithmetic series is 3, the last term is 136,
and the sum is 1,390, what are the first 3 terms?

Did I do this right?

$S_n \:=\tfrac{n}{2}(a_1+a_n) \quad\Rightarrow\quad 1390\:=\:n\left(\tfrac{139}{2}\right) \quad\Rightarrow\quad n\:=\:20$

$d \:=\:\frac{136-3}{n-1}\:=\: \frac{133}{20-1} \:=\: \frac{133}{19} \:=\: 7$

So it'd be: . $3+10+17 + \hdots + 136 \:=\: 1390$ . . . . Absolutely!
Don't forget to answer the question . . .

. . First three terms: . $3, 10, 17$