MHB Finding terms in arithmetic progressions

[doreent0722]

3). A company is to distribute \$36,000 in bonuses to its top five sales people. The fifth salesperson on the list will receive \$6,000 and the difference in bonus money between successively ranked salespeople is to be constant. find the bonus for each salesperson.

4). Find the third term of the recursively defined infinite sequence.
[a][/1]=3 [a][k+1]=[5][/ak]-2

 

[SuperSonic4]

3). A company is to distribute \$36,000 in bonuses to its top five sales people. The fifth salesperson on the list will receive \$6,000 and the difference in bonus money between successively ranked salespeople is to be constant. find the bonus for each salesperson.

4). Find the third term of the recursively defined infinite sequence.
[a][/1]=3 [a][k+1]=[5][/ak]-2

The sum of an arithmetic sequence is given by $$S_n = \dfrac{n}{2}(2a+(n-1)d)$$ where $$n$$ is the number of terms, $$a$$ is the first term and $$d$$ is the common difference.

You're given values for $$S_n$$, $$a$$ and $$n$$ in the question

 

[soroban]

Hello, doreent0722!

4) Find the third term of the recursively defined infinite sequence.
. . a_1=3,\;\;a_{k+1} = 5a_k -2

Do you understand what you are given?

The first term is 3.
Thereafter, each term is 5 times the preceding term, minus 2.

. . \begin{array}{ccccccc} a_1 &=& 3 \\ a_2 &=& 5(3)-2 &=& 13 \\ a_3&=& 5(13) - 2 &=& 63 & {\color{red}\Longleftarrow} \\ a_4 &=& 5(63)-2&=& 313 \\ a_5 &=& 5(313)-2 &=& 1563 \end{array}