Expert: Paul Klarreich - 1/28/2010

Question
1.the sum of the first 5 terms of an arithmetic series is 35 and the sum of the next 5 terms is 160. find the first term and the common difference.

2. the sum of the first 4 terms of an arithmetic series is 42 and the sum of the 3rd and 7th term is 46. find the sum of the first 29 terms.

3. the 20th term of an arithmetic series is 131 and the sum of the 6th to 10th terms inclusive is 235. find the sum of the first 20 terms.

4. the sum of 50 terms of an arithmetic series is 249 and the sum of 49 terms of the series is 233. find the 50th term of the series.


Answer
Questioner: nargs
Country: Australia
Category: Advanced Math
Private: No
Subject: hi
Question: 1.the sum of the first 5 terms of an arithmetic series is 35 and the sum of the next 5 terms is 160. find the first term and the common difference.

2. the sum of the first 4 terms of an arithmetic series is 42 and the sum of the 3rd and 7th term is 46. find the sum of the first 29 terms.

3. the 20th term of an arithmetic series is 131 and the sum of the 6th to 10th terms inclusive is 235. find the sum of the first 20 terms.

4. the sum of 50 terms of an arithmetic series is 249 and the sum of 49 terms of the series is 233. find the 50th term of the series.
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If you are studying these, you know that:

The first term is represented as  'a'.
The common difference is represented as  'd'.

The k-th term is  a + (k-1)d

The sum of n terms is  na +  dn(n-1)/2

(All of these are in your textbook.)

1. the sum of the first 5 terms of an arithmetic series is 35

So write:

n = 5 and 5a + d(5)(4)/2 = 35

and the sum of the next 5 terms is 160.

So the sum of the first TEN is 160 + 35, and

n = 10:  10a + d(10)(9)/2 = 195.

find the first term and the common difference.

You now have two equations:

5a  + 10d = 35
10a + 45d = 195.

Solve those.

I think the other three examples will go the same way.  If you have trouble, send me what you did and I'll see what I can do.