Given that √6,3√2,3√6,9√2 ...are the first 4 terms of an exponential sequence. Find in it
simplest form the 8term
looks like you have a = √6
and
ar = 3√2
r = 3√2/√6 = 3/√3 = 3/√3 * √3/√3 = √3
term(8) = ar^7
= √6(√3)^7
= √6(√3)^6 (√3)
= √18 * 27
= 81√2
procedures on how to solve this solution
Thanks
Can you teach me pls
Ans=81√2
That's the right answer
To find the 8th term of the exponential sequence, we need to find the common ratio first. The common ratio is found by dividing any term by its preceding term.
Let's take the second term, 3√2, and divide it by the first term, √6.
Common ratio = (3√2) / (√6) = (3√2 * (√6)) / (√6 * (√6)) = (3√12) / 6 = √12 / 2 = √4 * √3 / 2 = 2√3 / 2 = √3.
Now that we have the common ratio, we can find the 8th term by multiplying the 4th term, 9√2, by the common ratio raised to the power of 3 (8 - 4).
8th term = 9√2 * (√3)³ = 9√2 * 3 = 27√2.
Therefore, the 8th term of the exponential sequence is 27√2.