Answer:
29
Step-by-step explanation:
it's arithmetic sequence.
it has a basic equation like this
Un = a + (n-1)d
a = U1 = first number in sequence
Un = number in n-th term
d = difference
U9 = 101 + (9-1)(-9)
U9 = 101 - 72
U9 = 29
so the 9th term is 29
Answer:
The ninth term is 29.
Step-by-step explanation:
You can just keep subtracting 9 until you reach term number 9, but here is an explanation of how a sequence and a sequence formula works.
The first term is 101.
[tex] a_1 = 101 [/tex]
Then each term after that is 9 less than the previous term.
[tex] a_2 = 101 - 9 = 92 [/tex]
[tex] a_3 = 101 - 9 - 9 = 92 - 9 = 83 [/tex]
[tex] a_4 = 101 - 9 - 9 - 9 = 83 - 9 = 74 [/tex]
Now you begin to see a pattern.
Term 1 is simply 101 because that is what we were told about this sequence.
Term 2 is 9 subtracted from 101.
Term 3 is 2 times 9 subtracted from 101.
Term 4 is 3 times 9 subtracted from 101.
Each term after that is a multiple of 9 subtracted from 101. Which multiple of 9 is subtracted from 101 for each term? It is 9 multiplied by 1 less than the term number.
Look again at the terms above.
Term 1 is 101.
Term 2 is term number 2. What is subtracted from 101? 1, which is 1 less that the term number, multiplied by 9.
Term 3 is term number 3. 1 less than the term number is 2. That is the number of times you multiply 9 by and subtract from 101.
To write a formula for any term n, where n is 2 or greater, then term number n is
[tex] a_n = 101 - 9(n - 1) [/tex]
Now let's find term 9. We can use the formula above or we can reason the way I explained above. I'll show you both ways.
Reasoning:
Term 9 is term number 9. One less than 9 is 8. That means we start with 101 and we subtract 8 times 9.
[tex] a_9 = 101 - 8 \times 9 = 101 - 72 = 29 [/tex]
Formula:
[tex] a_n = 101 - 9(n - 1) [/tex]
n stands for the number of the term we want. We want term 9, so n = 9.
[tex] a_9 = 101 - 9(9 - 1) = 101 - 9(8) = 101 - 72 = 29 [/tex]
