We can find a formula for nth term of the given sequence as follows:
1, 5, 12, 22, 35
The 1st differences between terms:
4, 7, 10, 13
The 2nd differences :
3, 3, 3
Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form:
, where c is a constant. The coefficients a, b, and the constant c can be found.
We can form the following 3 equations with 3 unknowns a, b, c:
![1 = a\cdot1^2 + b\cdot1 + c\\5 = \cdot2^2 + b\cdot2 + c\\12 = a\cdot3^2 + b\cdot3 + c](https://tex.z-dn.net/?f=1%20%3D%20a%5Ccdot1%5E2%20%2B%20b%5Ccdot1%20%2B%20c%5C%5C5%20%3D%20%5Ccdot2%5E2%20%2B%20b%5Ccdot2%20%2B%20c%5C%5C12%20%3D%20a%5Ccdot3%5E2%20%2B%20b%5Ccdot3%20%2B%20c)
Solving for a, b, c, we get:
a = 3/2, b = -1/2, c = 0
Therefore, the nth term of the given sequence is:
![\boxed{ a_n = \dfrac{3}{2}n^2- \dfrac{1}{2} n}](https://tex.z-dn.net/?f=%5Cboxed%7B%20a_n%20%3D%20%5Cdfrac%7B3%7D%7B2%7Dn%5E2-%20%5Cdfrac%7B1%7D%7B2%7D%20n%7D)
Answer
33,33 and 22
Step-by-step explanation:
Answer:
The answer is t>0
Step-by-step explanation:
Let's solve your inequality step-by-step.
−2<3t−2
Step 1: Flip the equation.
3t−2>−2
Step 2: Add 2 to both sides.
3t−2+2>−2+2
3t>0
Step 3: Divide both sides by 3.
3t
/3 > 0/3
<em><u>t>0
</u></em>
Answer:
i think so
Step-by-step explanation:
Hello!
Answer:
1. ![\boxed{W=-6}](https://tex.z-dn.net/?f=%5Cboxed%7BW%3D-6%7D)
*The answer must have A NEGATIVE SIGN ONLY!*
2. ![\boxed{B=15}](https://tex.z-dn.net/?f=%5Cboxed%7BB%3D15%7D)
*The answer must have A POSITIVE SIGN ONLY!*
3. ![\boxed{N=-44}](https://tex.z-dn.net/?f=%5Cboxed%7BN%3D-44%7D)
*The answer must have a NEGATIVE SIGN ONLY!*
Step-by-step explanation:
1. 9w=-54
First, you divide by 9 both sides of an equation.
9w/9=-54/9
Simplify.
-54/9=-6
<u><em>W=-6 is the final answer.</em></u>
____________________________________
2. b-12=3
First you add by 12 both sides of an equation.
b-12+12=3+12
Add by the numbers from left/right.
3+12=15
<u><em>b=15 is the final answer.</em></u>
__________________________________________
3. n/4=-11
First you multiply by 4 both sides of an equation.
4n/4=4(-11)
Multiply by the numbers from left/right.
4*-11=-44
<u><em>n=-44 is the final answer.</em></u>
_____________________________
Hope this helps you!
Have a great day! :)
:D
-Charlie
Thanks!