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.

Answer 1

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!

Answer 2

105

Answer 3

Sorry but I really don't get it....I'm terrible at maths that's why😥

Answer 4

Plssssss can I get a more specific explanation I kind of have a problem with this topic

Answer 5

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