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The second,fourth and seventh terms of an arithmetic progression (A.P)are the first three.Consecutive terms of a geometric progression (G.P).If the common difference of the A.P...

      

The second,fourth and seventh terms of an arithmetic progression (A.P) are the first three consecutive terms of a geometric progression (G.P).If the common difference of A.P is 2,find:
(a)The common ratio of the G.P.
(b)The last term of the A.P given that there are eighteen terms.
(c)The sum of the first 14 terms of the G.P.

  

Answers


Seline
(a) a+d,a+3,a+6d
a+2,a+6,a+12

R= a+6/a+2 =a+12/9+6
(a+6)(a+6)=(a+2)(a+12)
a²+12a+36=a²+14a+24
36-24=14a-12a
12=12a
6=a
R= a+6/a+2 = 12/8 = 3/2 or 1.5
(b)last term=n th term
a+(n-1)d
h=18 6+(18-1)²
a=6 6+34
d=2 =40
(c)Term of the GP are 8,+12,+18,+....
A=8
r=3/2
h=14

Belan answered the question on February 28, 2019 at 15:14


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