SOLUTION: In an arithmetic sequence the 8th term is twice the 4th term and the 20th term is 40. Find the common difference and the sum of the terms from 8th to the 20th inclusive..

Question 792053: In an arithmetic sequence the 8th term is twice the 4th term and the 20th term is 40. Find the common difference and the sum of the terms from 8th to the 20th inclusive..
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
In an arithmetic sequence the 8th term is twice the 4th term and the 20th term is 40. Find the common difference and the sum of the terms from 8th to the 20th inclusive..
a= first term
n= number of terms
d = common difference
8th. Term
T8 = a+7d
T4 = a+3d
T8=2*T4
a+7d=2(a+3d)
a+7d=2a+6d
a-d=0
a=d
T20 = a+19d
-
Therefore T4 = 4a
T8=8a
T20=20a
40=20a
a=2
but a=d
so d=2
S20= 10(4+19*2)
=420
S10= =5(4+18)
S10 = 110
S20-S10= 420-110= 310

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