Further mathematics
posted by Tosin .
An exponential sequence of positive terms and a linear sequence have the same first term.the sum of their first terms is 3 the sum of their second terms is 3/2,and the sum of their third terms is 6.find their fifth terms.

Since the two sequences have the same first term, and they sum to 3, they both start with 3/2.
Let the arithmetic sequence be 3/2, 3/2 + d, 3/2 + 2d, ...
Let the geometric sequence be 3/2, 3/2 r, 3/2 r^2, ...
3/2 + d + 3/2 r = 3/2
so, d = 3/2 r
3/2 + 2d + 3/2 r^2 = 6
r = 3 or 1
d = 9/2 or 3/2
AS: 3/2, 3, 15/2, ...
GS: 3/2, 9/2, 27/2, ...
or
AS: 3/2, 3, 9/2, ...
GS: 3/2, 3/2, 3/2, ...
I assume you can make it to the 5th terms of each sequence.
Cool problem! 
105
Respond to this Question
Similar Questions

Further mathematics
An exponential sequence of positive terms and a linear sequence have the same first terms.the sum of their second terms is 3/2 and the sum of their third terms is 6.find their fifth terms. 
Maths
An arithmetic and a geometric sequence have the same first terms.(2)....and the same second term say X..The sum of the first 3 terms of the arithmetic sequence equals to the third term of the geometric sequence.Calculate the first … 
Maths
1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is … 
Math for Educators
The first difference of a sequence is 8, 12, 16, 20,... The sum of the first two terms of the original sequence is 14. Find the first three terms of the original sequence. The first term of the original sequence is? 
Further mathematics
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth … 
Mathematics arithmetic sequence
The sum of second and sixth terms of an arithmetic sequence is 4. The third term is 24 more than eleventh term. So determine the first three terms of the sequence. 
math
in an arithmetic sequence the common difference is equal to 2.the first term is also the first term of a geometric sequence. the sum of the first 3 terms of an arithmetic sequence and the sum of the first 9 terms of an arithmetic sequence … 
math
The first and second terms of an exponential sequence (G.P) are respectively the first and third terms of a linear sequence (A.P). The fourth term of the linear sequence is 10 and sum of its first five terms is 60. find (a) the first … 
furthermaths
The sum of the first ten terms of a linear sequence is 60 and the sum of the first fifteen terms of the sequence is 165.find the 18th term of the sequence. 
mathematics
The first, third and night terms of a linear sequence are the first three terms of an exponential sequence G. P if the seventh term of the linear sequence is 14.find the twentieth term of the linear sequence.