Question

Find the 86th of the arithmetic sequence 21, 15, 9, ..

Answer 1

The formula for finding the nth term of an arithmetic sequence is given as;

`\begin{gathered} nth=a+(n-1)d \\ \text{Where a is the first term, d is the common difference.} \\ \text{The common difference can be derived by subtracting each term from the next one} \\ \text{That is, the common difference is } \\ d=15-21=9-15=-6 \\ d=-6 \\ \text{Therefore, 86th term is calculated as;} \\ 86th=21+(86-1)-6 \\ 86th=21+\lbrack(85)-6\rbrack \\ 86th=21+\lbrack-510\rbrack \\ 86th=-489 \end{gathered}`

The 86th term is therefore, -489