SOLUTION: The second, fourth and eight terms of an A.p from the first three consecutive terms of a G.P. the sum of the third and fifth terms of the A.p is equal to 20. Find the (a) first 4

Algebra ->  Sequences-and-series -> SOLUTION: The second, fourth and eight terms of an A.p from the first three consecutive terms of a G.P. the sum of the third and fifth terms of the A.p is equal to 20. Find the (a) first 4      Log On


   

Question 1110258: The second, fourth and eight terms of an A.p from the first three consecutive terms of a G.P. the sum of the third and fifth terms of the A.p is equal to 20. Find the (a) first 4 terms of the A.p
(b) sum of the first 10 terms of the A.p.
Answer by mananth(16946) About Me  (Show Source):
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The second, fourth and eight terms of an A.p form the first three consecutive terms of a G.P. the sum of the third and fifth terms of the A.p is equal to 20. Find the (a) first 4 terms of the A.p
(b) sum of the first 10 terms of the A.p.
The second fourth and eighth terms can be written as
a+d , a+3d,a+7d
They are in GP
%28a%2B3d%29%2F%28a%2Bd%29+=+%28a%2B7d%29+%2F%28a%2B3d%29
%28a%2B3d%29%5E2+=+%28a%2Bd%29%28a%2B7d%29
a%5E2+%2B6ad%2B9d%5E2+=a%5E2+%2B8ad+%2B7d%5E2
2ad+=+2d%5E2
therefore a=d
as per second condition and a=d
a+2d +a+4d =20
8d =20
d=5/2 but d=a
First four terms are
t1=5/2
t2=5/2 +5/2 = 5
t3 = 5 + 5/2 = 15/2
t4 = 15/2 + 5/2 = 10
tn+=+%28n%2F2%29%28+2a%2B%28n-1%29d%29
S10+=+%2810%2F2%29%28+2%285%2F2%29+%2B+%2810-1%29%285%2F2%29%29
you can calculate S10

t8 = a+7d = 5/2 + 7(5/2) = 20