The first, second and eleventh terms of an arithmetic sequence with a common difference of 4 are the first, third and fifth terms of a geometric sequence. Find the sequence rule for the geometric and arithmetic sequences.
Thank you for any help!!
The first, second and eleventh terms of an arithmetic sequence with a common difference of 4 are the first, third and fifth terms of a geometric sequence. Find the sequence rule for the geometric and arithmetic sequences.
Thank you for any help!!
Let the arithmetic series be .
since the first terms of each sequence are the same, we know that the geometric sequence is of the form (the same )
this is for
hence, from the arithmetic sequence we have
from the geometric series we know that
now, know that you will be able to set up a system of equations to solve for , and hence answer the problem.
(i hope you know the formulas for an arithmetic sequence and geometric sequence to know how i got the expressions for and
In A.P:1st term=a, 2nd term=a+4,11th term=a+40
In G.P. 1st term=a, 3rd term=ar^2, 5th term=ar^4
Hence,
From (1):
Into (2):
If
I'm not sure what you mean by sequence rule, but I've calculated the original term and ratio for the G.P, so I'm not what else you need.
A.P.:
G.P.: