You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
Intermediate Algebra: girlpower
- Thread starter girlpower
- Start date
I need help on this problem:
If the 4th and 9th terms of an arithmetic sequence are 36 and 91. what is the difference between consecutive terms?
There are a couple ways you can solve this problem, but let me see what you have tried so far.
Hello, girlpower!
The very least you could do is draw a "picture".
. . \(\displaystyle \begin{array}{cccccc}\;\;36\;\; & 36+d & 36+2d & 36+3d & 36+4d & 36+5d \\ --- & --- & --- & --- & --- & --- \\ 4^{th} & 5^{th} & 6^{th} & 7^{th} & 8^{th} & 9^{th} \end{array}\)
\(\displaystyle \text{The }9^{th}\text{ term is 91: }\;\;36 + 5d \:=\:91 \quad\Rightarrow\quad 5d \,=\,55 \quad\Rightarrow\quad d \,=\,11\)
The 4th and 9th terms of an arithmetic sequence are 36 and 91.
What is the difference between consecutive terms?
The very least you could do is draw a "picture".
. . \(\displaystyle \begin{array}{cccccc}\;\;36\;\; & 36+d & 36+2d & 36+3d & 36+4d & 36+5d \\ --- & --- & --- & --- & --- & --- \\ 4^{th} & 5^{th} & 6^{th} & 7^{th} & 8^{th} & 9^{th} \end{array}\)
\(\displaystyle \text{The }9^{th}\text{ term is 91: }\;\;36 + 5d \:=\:91 \quad\Rightarrow\quad 5d \,=\,55 \quad\Rightarrow\quad d \,=\,11\)
I need help on this problem:
If the 4th and 9th terms of an arithmetic sequence are 36 and 91. what is the difference between consecutive terms?
Hi girlpower.
Since Soroban already provided the solution, let me offer a tip in solving this kind of problem when the idea of drawing a picture is not an option (such as when you have two terms that are far apart like say the 8th term and the 756th term).
The number of "d's" that you add to the first term you have, in your case, 36, is the difference in the term numbers. In other words, you have the 4th term and the 9th term, thus 9-4 = 5 so you add 5 "d's" to 36.
Thus, 36 + 5d = 91 and then you solve for d which is 11.
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,760
To go from the 4th to the 9th term, you have to take 9- 4= 5 'steps'. And you will have added 91- 36= 55. Since this is an arithmetic sequence, the difference is constant- call it "d". Adding d 5 times means you have added 5d and so 5d= 55.I need help on this problem:
If the 4th and 9th terms of an arithmetic sequence are 36 and 91. what is the difference between consecutive terms?