Asked 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.
Answered by Steve
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!
Answered by oladepo oluwatobi
105
Answered by Nifemi
Sorry but I really don't get it....I'm terrible at maths that's why😥
Answered by Faith
Plssssss can I get a more specific explanation I kind of have a problem with this topic
Answered by Fimmy
An exponential sequence of positive terms and a linear sequence have the same first term. The sum of their first term is 3, the sum of their second term is 3/2, and the sum of their third term is 6. Find the sum of their fifth terms