Task 6
Finite Mathematics Task 6: Number Patterns
A. Provide the first five terms of an arithmetic or geometric sequence that has a first term
higher than 10 and a common difference or ratio that is positive but not 1.
a1= 15, a2=20, a3=25, a 4=30, a5 =35
1. Using the general formula for either the arithmetic or geometric sequence, derive
the specific nth term formula for the sequence from part A, showing all steps.
an =a1 +( n โ1 ) d
an =15 +( nโ1 ) ( 5 )
an =15 +5 nโ5
an =5 n+10
2. Find the 30th term of the sequence from part A, using the nth term formula from part A1
and showing all work.
an =a1 +( n โ1 ) d a30=5 ( 30 )+10
an =15 +( nโ1 ) ( 5 ) a30=150 + 10
an =15 +5 nโ5 a30=160
an =5 n+10
B. Explain how to use patterns or sequences to determine the last digit of the number 7N, where
N is the four-digit year of your birth.
In determining the last digit of the number 7 N , I have to first substitute my birth
year into the equation for N. The problem will now read 71979 . I would first try to figure out
