The first,third and seventh term of an arithmetic progression form three consecutive terms of a geometric progression. If the first, second terms of the arithmetic progression is 6. Find its first term and common difference.
(F + 6*D) / (F + 2*D)==(F + 2*D) - 6, solve for F, D
F ==4 - this is the first term of the AP
D==2 - this is the common difference of the AP
The AP looks like this:
4, 6, 8, 10, 12, 14, 16, 18, 20.....and so on
The 3 consecutive terms of the GP from the above AP are:
4, 8, 16........and so on
The common ratio of the GP ==2
