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.
1. t-3,t-2, t-1, t...
2. 3/4,1/2,1/3,2/9...
3. 1,-3/2,2,-5/2....
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kendrick/richard/thomas -- You really need to just pick a name and stay with it!
i need help please!
To be an arithmetic sequence, the difference between any term and its previous term is a constant.
e.g. 3, 5, 7, 9 , ... the common difference is 2
To be geometric, if you divide any term by its previous term you will get a common ratio,
e.g.
3, 12, 48, ...
12/3 = 4, 48/12 = 4 etc
I will do #2, you do the others
test for arithmetic:
is 1/2 - 3/4 = 1/3 - 1/2
is -1/4 = -1/6 ? NO, so NOT arithmetic
test for geometric:
is (1/2)/(3/4) = (1/3) / (1/2) ?
is (1/2)(4/3) = (1/3)(2/1) ?
is 2/3 = 2/3 ? Yes!!
so #2 is a geometric sequence
for number is it t the common difference?
i cant find a common ratio for number three, is it neither?
To identify if a given sequence is arithmetic or geometric, we need to examine the differences or ratios between consecutive terms.
1. t-3, t-2, t-1, t...
In this sequence, the difference between consecutive terms is always 1. Therefore, this is an arithmetic sequence. To find the next term, we add 1 to the last term: t + 1. The nth term of this arithmetic sequence can be written as t - 3 + (n - 1) * 1.
2. 3/4, 1/2, 1/3, 2/9...
In this sequence, the ratio between consecutive terms is not constant, so it is neither arithmetic nor geometric.
3. 1, -3/2, 2, -5/2...
In this sequence, the pattern alternates between adding 5/2 and subtracting 7/2. The difference between consecutive terms is not constant, so it is neither arithmetic nor geometric.
To summarize:
1. Arithmetic: Next term = t + 1; nth term = t - 3 + (n - 1) * 1.
2. Neither arithmetic nor geometric.
3. Neither arithmetic nor geometric.