SOLUTION: two arithmetic series are such that their common difference are 9 and 3 respectively. If their first terms are 2 and 5 respectively, find the number of terms of each series that wo

Question 858287: two arithmetic series are such that their common difference are 9 and 3 respectively. If their first terms are 2 and 5 respectively, find the number of terms of each series that would give a common sum.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
two arithmetic series are such that their common difference are 9 and 3 respectively. If their first terms are 2 and 5 respectively, find the number of terms of each series that would give a common sum.

Let Sn be the sum of first series d=9, a=2
S'n be the sum of second series. d=3, a=5
Sn = n/2(2a1+(n-1)d)
Sn = n/2 (2*2+(n-1) 9)
Sn = n/2( 4+9n-9)
Sn = n/2(4n-5)
Find S'n
S'n = n/2(2*5+(n-1)*3)
S'n = n/2(10+3n-3)
S'n = n/2(3n+7)
Sn=S'n
n/2(4n-5)=n/2(3n+7)
4n-5 = 3n+7
4n-3n=12
n=12
For the 12 th. term the sums are equal

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