<PRE><B>Question 1202406</B>
The second and fifth terms are in a geometric progression are 12 and 40.5 respectively. Find the first term and the common ratio. Hence, write down an expression for the nth term.

nth term of a GP is an=ar^(n-1)

2nd term

a2 = a*r^(2-1)

12= a*r

5th term

40.5= a*r^(5-1)

40.5 = ar^4

40.5= ar*r^3   

40.5 = 12*r^3 (ar=12)

40.5/12 = r^3

3.375=r^3

3 15/40=r^3
135/40 =r^3
27/8 =r^3
cube root

r= 3/2


ar= 12 
r = 3/2

a*3/2=12

a=8

an = a*r^(n-1)

an = 8*3/2 ^(n-1)

 

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