Answer:
Find the 13th term in the following arithmetic sequence
2, 10, 18, 26 ...192 is the 13th term
Answer:C.11 in
explanation:Hope I helped:)
Answer:
t(n) = 2n² + n - 3
Step-by-step explanation:
<u>Given sequence: </u>
Find the formula for nth term t(n)
<h3>Solution</h3>
<u>Sequence is neither arithmetic nor geometric, analyzing:</u>
<u>First level difference</u>
<u>Second level difference</u>
<u>As there are two levels, the formula should be in the form of:</u>
<u>Trying the formula with the known terms:</u>
- t(2) = 4a + 2b + c = 7 ⇒ 3a + b = 7
- t(3) = 9a + 3b + c = 18 ⇒ 3(3a+b) + c = 18 ⇒ 21 + c = 18 ⇒ c = -3
<u>Going back to previous equations to find remaining coefficients:</u>
- t(1) ⇒ a+ b = 3 ⇒ t(2) = 2a + (a+b) = 7 ⇒2a + 3 = 7 ⇒ a= 2 ⇒ b = 1
<u>So the formula becomes:</u>
t(n) = 2n² + n - 3
Take the fouth square root of both sides
![\sqrt[4]{{x}^{4} } = \sqrt[4]{24}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B%7Bx%7D%5E%7B4%7D%20%7D%20%20%3D%20%20%5Csqrt%5B4%5D%7B24%7D%20)
so
![x = \sqrt[4]{24} \: or \: x = - \sqrt[4]{24}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csqrt%5B4%5D%7B24%7D%20%20%5C%3A%20or%20%5C%3A%20%20x%20%3D%20%20-%20%20%5Csqrt%5B4%5D%7B24%7D%20)
