SOLUTION: 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.

Question 1202406: 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.
Found 3 solutions by greenestamps, ikleyn, mananth:
Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!

Use the standard convention of a for the first term and r for the common ratio.

First term:
Second term:
Fifth term:

The ratio of the fifth and second terms is the common ratio, cubed. Use that to determine the common ratio.

The first term is the second term, divided by the common ratio.

ANSWERS:
1st term: 8
formula for n-th term (ar^(n-1):

Answer by ikleyn(52920)   (Show Source): You can put this solution on YOUR website!
.
The second and fifth terms 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.
~~~~~~~~~~~~~~~~~~~~~~

Write the terms in standard form = a*r, = , Take the ratio = = = = 3.375. It implies r = = 1.5. Thus the common ratio is r= 1.5. Now the first term is a = = = 8. The expression for the n-th term is = = .

Solved.     //     All questions are answered.

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On geometric progressions, see introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

Learn the subject from there.

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
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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