SOLUTION: (a)if log x , log(x+2) , log(x+16) are three consecutive terms of an AP, find the value of x. (B)the sixth terms of an AP is Twice the Second term and the fifth term exceeds the f

Algebra ->  Sequences-and-series -> SOLUTION: (a)if log x , log(x+2) , log(x+16) are three consecutive terms of an AP, find the value of x. (B)the sixth terms of an AP is Twice the Second term and the fifth term exceeds the f      Log On


   

Question 637911: (a)if log x , log(x+2) , log(x+16) are three consecutive terms of an AP, find the value of x.
(B)the sixth terms of an AP is Twice the Second term and the fifth term exceeds the first term by 10.find first term and the common difference.
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
(a) log(x+2) - log x = log(x + 16) - log (x + 2)
log [(x + 2)/x] = log [(x + 16)/(x + 2)]
+%28x+%2B+2%29%2Fx+=+%28x+%2B+16%29%2F%28x+%2B+2%29+, cross multiply
+%28x+%2B+2%29%5E2+=+x%28x+%2B+16%29+
+x%5E2+%2B+4x+%2B+4+=+x%5E2+%2B+16x
+12x+=+4
Answer: highlight%28x+=+1%2F3%29
(b) Let x be the first term and k be the common difference.
6th term = x + 5k
2nd term = x + k
5th term = x + 4k
Equations:
(x + 5k) = 2(x + k) or x - 3k = 0
(x + 4k) - x = 10 or 4k = 10, therefore k = 2.5
So x - 3(2.5) = 0, therefore x = 7.5

Answer: The first term is 7.5 and the common difference is 2.5.