Question

5.2.3 recursive sequences homework
5.2a) and colin were trying to challenge each other with equations for sequences. avery wrote a function that colin wrote.
t(n) = 4.5n - 8
write the first 4 terms for the sequence.
what would avery do to write the 15th term of the sequence?

Explanation:

Step1: Find 1st term (n=1)

Substitute $n=1$ into $t(n)=4.5n-8$:
$t(1)=4.5(1)-8=4.5-8=-3.5$

Step2: Find 2nd term (n=2)

Substitute $n=2$ into $t(n)=4.5n-8$:
$t(2)=4.5(2)-8=9-8=1$

Step3: Find 3rd term (n=3)

Substitute $n=3$ into $t(n)=4.5n-8$:
$t(3)=4.5(3)-8=13.5-8=5.5$

Step4: Find 4th term (n=4)

Substitute $n=4$ into $t(n)=4.5n-8$:
$t(4)=4.5(4)-8=18-8=10$

Step5: Find 13th term (n=13)

Substitute $n=13$ into $t(n)=4.5n-8$:
$t(13)=4.5(13)-8=58.5-8=50.5$

Answer:

First 4 terms: $-3.5, 1, 5.5, 10$
To find the 13th term, substitute $n=13$ into the explicit formula; the 13th term is $50.5$