The 5th, 8th and 11th terms of a GP are a, b, c respectively. Show that b2 = ac

It is given in the question that 5th, 8th and 11th terms of GP are a, b and c respectively.


Let us assume the GP is A, AR, AR2, and AR3….


So, the nth term of this GP is an = ARn-1


Now, 5th term, a5 = AR4 = a (1)


8th term, a8 = AR7 = b (2)


11th term, a11 = AR10 = c (3)


Dividing equation (3) by (2) and (2) by (1),


(4)


(5)


So, both equation (4) and (5) gives the value of R3. So we can equate them.


,


b2 = ac,


Hence proved.


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