arithmetic sequence sum

Makito

New member
Joined
Apr 7, 2019
Messages
1
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
Joined
Feb 17, 2004
Messages
1,724
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
Joined
Mar 25, 2016
Messages
1,148
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
Joined
Dec 30, 2014
Messages
3,652
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
Joined
Dec 30, 2014
Messages
3,652
CLEARLY stated:
We have an arithmetic sequence.
Sum of first 2 terms = 13
4th term = -1

Go here :

Come back if you have questions.
No no, only Subhotosh can recommend such videos. You can get into great trouble doing this. No need to worry as I won't report you.
BTW would you be interested in purchasing a bridge I have for sale, it's called the Brooklyn Bridge
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,724
BTW would you be interested in purchasing a bridge I have for sale, it's called the Brooklyn Bridge
HOKAY: a dollar down and a dollar a week;
I'll have my people contact your people...
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
8,319
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!
 
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