anonymous
  • anonymous
How do I find the last term of an arithmetic sequence when the first term is 2, and the fourth term is 11.?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Last term???
anonymous
  • anonymous
They didn't give us a last term.. The problem states: The first term of an arithmetic sequence is 2, and the fourth term is 11. Find the sum of the first 50 terms. Obviously, I'm using sigma notation, but I don't have the last term to plug into it....
anonymous
  • anonymous
|dw:1378652521007:dw|

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anonymous
  • anonymous
Oh,now it can be solved as easily as possible ... In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2. If the initial term of an arithmetic progression is a_1 and the common difference of successive members is d, then the nth term of the sequence (a_n) is given by: a-n= a-1 + (n-1)d now keep it in your mind 'n' we use it later.. The sum of the members of a finite arithmetic progression (S-n) is called an arithmetic series. S-n=n/2(a-1+a-n) You need to find: 1) d 2) the last term
anonymous
  • anonymous
I am aware of that information, but thank you for refreshing it for me. So, how do I find the common difference if they give us only two numbers?
anonymous
  • anonymous
from relation 1... a-4=a-1+(4-1)d ---> 11=2+3d --> d=3
anonymous
  • anonymous
Perfect. That works. a1=2 a2=5 a3=8 a4=11
anonymous
  • anonymous
You need to find a-50 if you wanta calculate the sum of the first 50 terms.... a-50= a-1 +(50-1)3 S-50-50/2(2+a-50) ok???
anonymous
  • anonymous
You need to find a-50 if you wanta calculate the sum of the first 50 terms.... a-50= a-1 +(50-1)3 --> a-50= 2+147=149 S-50=50/2(2+a-50) ---> S-50( the sum of first 50 terms)=50/2(2+149)=3775 ok???
anonymous
  • anonymous
So, the 50th term is 149, and the sum is 3775?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
I have to go. take care!!
anonymous
  • anonymous
Perfect! Thanks for your help. I just double checked the answer with sigma and it works.

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