SOLUTION: Three numbers form an arithmetic sequence, common difference being 11. If first number is decreased by 6, second number decreased by 1, and third number doubled, resulting numbers

Question 254675: Three numbers form an arithmetic sequence, common difference being 11. If first number is decreased by 6, second number decreased by 1, and third number doubled, resulting numbers form a geometric sequence. determine the numbers that form the arithmetic sequence
Answer is -26, -15, -4, 14, 25, 36
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
Let the first term be A
Let the second term be A + 11
Let the third term be A + 22
we know that common difference, d, is 11.
--
A - 6, A + 10, 2(A+22)
is now a geometric sequence. They have common ratios which can be expressed as
(A+10)/(A-6) = (2A+44)/(A+10)
Cross multiplying, we get
(A+10)^2 = (2A+44)(A-6)
A^2 + 20A + 100 = 2A^2 + 32A -264
set = 0 as
A^2 + 12A -364 = 0
(A - 14)(a + 26) = 0
A = 14 or A = -26
--
If A = 14, then the arithmetic sequence is
14, 25, 36
and the geometric sequence is
8, 24, 72
--
If A = -26, then the arithmetic sequence is
-26, -15, -4
and the geometric sequence is
-32, -16, -8
RELATED QUESTIONS
Three numbers are in an arithmetic progression with a common difference of 6. If 4 is... (answered by greenestamps)

Three numbers form an arithmetic sequence having a common difference of 4, if the first... (answered by KMST)

Three numbers form an arithmetic sequence. The first term minus the third term is 8. When (answered by htmentor)

The sum of three numbers in arithmetic sequence is 24 . If the first number is decreased (answered by richard1234)

The first,third and eight term of an arithmetic sequence form the first three terms of a... (answered by richwmiller)

the sum of the first and last terms of an arithmetic progression is 42.the sum of all the (answered by ikleyn)

Three positive numbers form an arithmetic progression; their sum is 18. If the first... (answered by ikleyn)

The digits of a three digit number form an arithmetic progression. If the first and... (answered by Edwin McCravy)