Question

Two arithmetic series are such that their common differences 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 1

Answer:

number of terms=n=2

Step-by-step explanation:

in first series

a=2

d=9

in second series

a=5

d=3

Sn=n/2(2a+n-1)d

equalise Sn for first series and second series

therefore we get

n/2(2.2+(n-1)9)=n/2(2.5+(n-1)3)

4+9n-9=10+3n-3(on both sides n/2 get cancelled)

9n-5=3n+7

9n-3n=7+5

6n=12

n=2

sum of two terms are equal for each series