# arithmetic sequence sum

#### Makito

##### New member
Hi,

If I know that a1 + a2 is 13

And a4 is -1

How can I get sum number of first 30 numbers in sequence?

Is there any online calculator that can help me?

#### Denis

##### Senior Member
If I know that a1 + a2 is 13
And a4 is -1
How can I get sum number of first 30 numbers in sequence?
CLEARLY stated:
We have an arithmetic sequence.
Sum of first 2 terms = 13
4th term = -1

Go here :

Come back if you have questions.

#### ksdhart2

##### Senior Member
Although you never explicitly stated such in the body of your message, I can infer from your title that $$a_n$$ is meant to be an arithmetic sequence. With that in mind, we can use what you (should) already know about arithmetic sequences: They have some starting value and then each successive term is some common difference more/less than the previous term.

We're given that $$a_4 = -1$$ but we're not told a common difference. Hmm... well, the most important principle in all of algebra is that if we don't know a value, we can give that value a name so as to make talking about it and working with it easier. Let $$d$$ be the common difference of the sequence $$a_n$$. Can you see why that means we can say that $$a_4 = a_3 + d \implies -1 = a_3 + d$$? How can you rearrange that equation such that we have $$a_3 = (\text{something})$$? Using this result, what can you say about $$a_2$$? And then what can you say about $$a_1$$? Finally, what do you get when you plug these values into the first given equation that $$a_1 + a_2 = 13$$? Where does that lead you?

#### Jomo

##### Elite Member
Hi,

If I know that a1 + a2 is 13

And a4 is -1

How can I get sum number of first 30 numbers in sequence?

Is there any online calculator that can help me?
a1 + a2 is 13 translates into (a1)+ (a1+d) = (2a1+d) = 13
Now a4 =a1 + 3d = -1

Now solve 2a1+d = 13 and a1 + 3d = -1 for a1 and d

Can you finish from here?

Last edited:

#### Jomo

##### Elite Member
CLEARLY stated:
We have an arithmetic sequence.
Sum of first 2 terms = 13
4th term = -1

Go here :

Come back if you have questions.
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#### Denis

##### Senior Member
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#### pka

##### Elite Member
If I know that a1 + a2 is 13
And a4 is -1
How can I get sum number of first 30 numbers in sequence?
People who need a calculator do not know. You Makito want to know.
Arithmetic series have only two essential parts: a first term and a common different.
Suppose that the first term is $$\displaystyle a_1$$ and a common different is $$\displaystyle d$$.
Then the sequence is $$\displaystyle a_n=a_1+ [(n-1)d]$$
Now the sum $$\displaystyle {S_n} = \sum\limits_{k = 1}^n {{a_1}(k - 1)d} = {a_1}d\sum\limits_{k = 1}^n {(k - 1)} = {a_1}d\frac{{(n - 1)n}}{2}$$
If $$\displaystyle a_1+a_2=13$$ then $$\displaystyle a_1+(a_1+d)=13 \text{ or }2a_1+d=13$$
AND $$\displaystyle a_4=a_1+(4-1)d=-1$$
Now Show us what you can do with his help!