SOLUTION: In an arithmetic progression, the sum of the first ten terms is 50 and the 5th term is three times the second term. Find the A. First term. B. Common difference. C. The sum of the

Question 1162188: In an arithmetic progression, the sum of the first ten terms is 50 and the 5th term is three times the second term. Find the A. First term. B. Common difference. C. The sum of the first 100 terms

Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

an arithmetic progression:
, , ,.... where is the first term and is Common difference

nth term formula:

Denote this partial sum by . Then
,where is the number of terms, is the first term and is the last term

given: the sum of the first ten terms is
->

.......solve for
....

.....eq.1

the 5th term is three times the second term:
-> and

......... ..eq.2

substitute in eq1
.....eq.1

-> First term
go to eq.2
......... ..eq.2

->Common difference

nth term formula:

first terms are:
, , , ,,,, ,,
or
, , , ,,,, ,,
check their sum:

-> true

The sum of the first terms:
first find th term:
->
then the sum is:

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

In an arithmetic progression, the sum of the first ten terms is 50 and the 5th term is three times the second term. Find the A. First term. B. Common difference. C. The sum of the first 100 terms

Sum of an A.P.:
------ eq (i)
Term of an A.P.:

Since , we get:
10 = d + 9d ---- Substituting in eq (i)
10 = 10d

Sum of an A.P.:

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