Identify if the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic or geometric, then find the next term. and write the nth term.
. t-3,t-2, t-1, t...
. 1,-3/2,2,-5/2....
see related questions below
below where?
what is the common difference then for the first one?
suppose the terms were
-3,-2,-1,0,...
would that be hard tto figure out? Well, it's the same here:
(t-2)-(t-3) = 1
(t-1)-(t-2) = 1
The common ratios for the 2nd one are found by dividing each term by the previous one:
1,-3/2,2,-5/2
(-3/2)/(1) = -3/2
2/(-3/2) = -4/3
(-5/2)/(2) = -5/4
the ratios are not the same.
As for the related questions, "below" means you need to scroll down to where it plainly says -- wait for it --
Related Questions
sheesh!
i have another question: Identify if the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic or geometric, then find the next term. and write the nth term.
t^3,t^2,t,1.... is it geometric or arithmetic?
thank you
To determine whether a sequence is arithmetic, geometric, or neither, we need to analyze the pattern between the terms.
1. For the sequence t-3, t-2, t-1, t...
This sequence is arithmetic because the difference between consecutive terms is constant. The common difference is 1, as each term is obtained by adding 1 to the previous term. Therefore, the next term would be t + 1.
The nth term of an arithmetic sequence can be found using the formula: an = a1 + (n - 1) * d, where a1 is the first term and d is the common difference. In this case, the first term is t-3 and the common difference is 1. The nth term would be t - 3 + (n - 1) * 1, which simplifies to t - 3 + n - 1, or t + n - 4.
2. For the sequence 1, -3/2, 2, -5/2...
This sequence is neither arithmetic nor geometric because there is no consistent pattern between the terms. The differences between consecutive terms (-4/2, 5/2, -7/2, etc.) are not constant, so it is not an arithmetic sequence. Additionally, the ratios between consecutive terms (-3/2 ÷ 1 = -3/2, 2 ÷ -3/2 = -4/3, etc.) are not constant, so it is not a geometric sequence. As a result, we cannot determine the next term or write a general formula for the nth term of this sequence.