Question

Each term in the sequence below is nine less than the previous term. What is the ninth term in the sequence? 101, 92, 83, 74,... Plz explain

Answer 1

The ninth term is 29.

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.

`a_1 = 101`

Then each term after that is 9 less than the previous term.

`a_2 = 101 - 9 = 92`

`a_3 = 101 - 9 - 9 = 92 - 9 = 83`

`a_4 = 101 - 9 - 9 - 9 = 83 - 9 = 74`

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

`a_n = 101 - 9(n - 1)`

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.

`a_9 = 101 - 8 * 9 = 101 - 72 = 29`

Formula:

`a_n = 101 - 9(n - 1)`

n stands for the number of the term we want. We want term 9, so n = 9.

`a_9 = 101 - 9(9 - 1) = 101 - 9(8) = 101 - 72 = 29`

Answer 2

29

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