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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.

 Aug 19, 2022
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(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

 Aug 19, 2022
edited by Guest  Aug 19, 2022

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