AS Maths Core 2 hard sequence question

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willmatthews26
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Hi could somebody please help me with this sequence question:

Three consecutive terms of a geometric progression also form the 2nd 4th and 7th terms of an arithmetic progression.

1.) what is the common ratio of the geometric sequence

2.) three consecutive terms of an AP have a sum of 36 and a product of 1428. find the three terms.

3.)The sum of the first 2 terms of a geometric progression is 9, and the sum of the first 4 terms is 45. calculate the 2 possible values of the 5th term in the progression.

Many thanks
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NotNotBatman
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In the arithmetic sequence,


 U_2 = a +d\\U_4= a+3d\\ U_7 = a+6d

In a geometric progression the common ratio is found by dividing a term in the sequence with the term immediately preceding. so if  r is the common ratio, then  r= \frac{U_{n+1}}{U_n}

So, r = \frac{U_4}{U_2} and r=\frac{U_7}{U_4} us this to form an equation in  a and  d and solve simultaneously, then use the AP to find the common ratio.
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