Question

Three numbers whose common difference is 3 are in an arithmetic sequence. If the first number is left unchanged and 1 is subtracted from the second and 2 is added to the third the resulting three numbers are in a geometric sequence.

1. Find X

2. Find the original number

3. Find the number in the geometric sequence

4. What would the 10th term of the arithmetic sequence be?

5. What number term would 387,420,489 of the geometric sequence be?

Answer 1

an = a1 + (n-1)3
a2 -1 = a1 + 2
a3 +2 = a1 +8
a1, a2 -1, a3 +2 ... is geo seq
common ratio = [a2 -1]/a1 = [a3 +2]/[a2 -1]
[a1 + 2]/a1 = [a1 +8 ]/[a1 + 2]
[a1 + 2]^2 = a1 [a1 +8 ]
a1^2 + 4a1 + 4 = a1^2 + 8a1
a1 = 1
an = 1 + (n-1)3
geo seq 1, 3, 9,... an = 3^(n-1)