SOLUTION: Please help If the number of terms of an Arithmetic sequence is 15 and the value of it's middle term is 10 then find the sum of it's terms is there any rule that i can solve it wit

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Question 745077: Please help If the number of terms of an Arithmetic sequence is 15 and the value of it's middle term is 10 then find the sum of it's terms is there any rule that i can solve it with?? Thanks
Found 2 solutions by sachi, mananth:
Answer by sachi(548) (Show Source):
You can put this solution on YOUR website!
the number of terms of an Arithmetic sequence is 15
so the middle term= (15+1)/2=8th term (+1 for odd no of terms)
so t8=a+(8-1)d=a+7d (a,d being 1st term & common difference)
the value of it's middle term is 10
so a+7d=10.........1
the sum of it's terms is S15=(15/2)*(2a+[15-1]d)=7.5*(2a+14d)=7.5*2*(a+7d)
=7.5*2*10=150 putting the value from eqn 1
so the sum =150

Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!

The nth term of an AP is given by the formula Tn = a+(n-1)d
t15 = a+14d
The middle term is the 8th term
T8=a+7d
10=a+7d
multiply by 2
20=2(a+7d)
20=2a+14d

Sum of n terms = Sn = n/2[2a+(n-1)d]
s15 = 15/2[2a+(15-1)d]
S15= 15/2[2a+14d]
but 2a+14d=20
S15=15/2( 20)
S15=150
sum of 15 terms = 150