Consider the finite linear pattern:20;17;14...;-103 . write down the 4th term of the pattern

Question

Determine the expression for the nth term

 

Answer 1

\(a_4=11\)

 

Explanation:

Given the sequence \(20;17;14;\ldots -103 \dots\) it can be seen that the common difference is \(-3\) i.e. \(a_{n+1}-a_n=3\)

\[20-17=3\]

\[17-14=3\]

 

This is a decreasing sequence i.e. decreasing by 3 with each term.

the fourth term is calculated using the following linear equation:

\[14-a_4=3\]

\[a_4=14-3\]

\[\therefore a_4=11\]

Answer 2

The nth term is given by the formula:

\[T_n=a+(n-1) d\]

where

\(a\) is the first term

\(d\) is the common difference

\[T_n = 20+(4-1)-3\]

\[T_n =20-9=11\]