Answer :
Since there are only three terms and they repeat we can easily figure this out.
To do that all we have to do is determine how far away 91 is from a multiple of three. If it lands on a multiple of three it will be -12. If it is two above a multiple of three it will be eight. If it is one above a multiple of three it will be 28.
So the 91st term in one above a multiple of three the answer will be 28.
91st term of the arithmetic sequence 28, 8, -12, .. is - 1772
What is an arithmatic sequence?
A sequence of numbers which increases or decreases by a constant amount each term is called an arithmatic sequence.
- That common amount (term) is called common difference, which can be calculated by subtracting a term from its next term.
How to find what is the 91st term of the given arithmetic sequence ?
The given arithmatic sequence is 28, 8, -12......
- Common difference = (8 - 28) = -20
- We can find any term ( nth term) of ta given arithmatic sequence by using the formula ,
[tex]T_{n}[/tex] = a + (n-1)d
where, [tex]T_{n}[/tex] is the nth term
a is the first term
d is the common difference
- Using that formula we can write,
[tex]T_{91}[/tex] = 28 + (91 - 1)(-20) = -1772
∴ 91st term of the arithmetic sequence 28, 8, -12, .. is - 1772
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