Question

1. What is the 8th term in the sequence?

Note: Use the explicit rule.

an=25−3n

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a8=

2. Which answer is the explicit rule for the sequence: 13, 10.5, 8, 5.5, 3, 0.5, ...

A. an=15.5−2.5n

B. an=15+2.5n

C. an=15−2.5n

D. an=15.5+2.5n

3. A coin collector has 1044 coins. Each month, the coin collector purchases 9 more coins.



How many coins will the coin collector have after 34 months?



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4. What is the recursive rule for an=3n+5

A. a1=8;an=an−1+3

B. a1=5;an=an−1+3

C. a1=8;an=an−1+5

D. a1=3;an=an−1+5

Answer 1

The asnwer to the following set of questions are as follows:

1. The 8th term of the sequence would be 1.

2. A. an=15.5−2.5n

3. The coin collector will have 1350 coins after 34 months

4. The recursive rule for an=3n+5 would be a1=8;an=an−1+3

I hope my answer has come to your help. God bless and have a nice day ahead!

Answer 2

Explanation:

(1) Using the rule
`a_n=25-3n`

put n=8 in the above formula we get

`a_8=25-3(8)=1`

Hence,
`a_8=1`

(2) The given sequence has common difference -2.5

common difference that is
`d=a_2-a_1`

We will use the formula of AP which is

`a_n=a+(n-1)d`

Here, a= 13, d=-2.5 and n=n on substituting the values in the formula we get

`a_n=13+(n-1)(-2.5)`

`a_n=15.5-2.5n`

Hence, Option A

(3)From the given information we can conclude

`a=1044,d=9,n=34`

We have to find
`a_n`

On substituting the values we get

`a_n=1044+(34-1)(9)`

`a_n=1044+297`

`a_n=1341` coins the coin collector will have.

(4) Recursive rule for
`a_n=3n+5` will be

Put n=1 in the given formula we get

`a_1=3(1)+5=8`

When n=2 we get

`a_2=3(2)+5=11`

When n=3 we get

`a_3=3(3)+5=14`

Hence, option A that is
`a_1=8;a_n=a_(n-1)+3`