Question

Find the 19th term of a sequence where the first term is 2 and the common difference is -3

Answer 1

`n^(th)\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^(th)\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=2\\ d=-3\\ n=19 \end{cases} \\\\\\ a_(19)=2+(19-1)(-3)\implies a_(19)=2+(18)(-3)\implies a_(19)=-52`

Answer 2

-52.

Explanation:

Definition:

Sequence: A list of numbers in a specific order.

First term: The first number in a sequence.

Common difference: The difference between two consecutive terms in a sequence.

nth term: The term in a sequence that is n terms away from the first term.

Solution:

In order to find the 19th term of a sequence where the first term is 2 and the common difference is -3, we can use the following formula:

nth term = first term + (n - 1) × common difference

In this case, the first term is 2, the common difference is -3, and we are looking for the 19th term.

Substituting these values into the formula, we get:

19th term = 2 + (19 - 1) × -3

19th term = 2 - 54

19th term = -52

Therefore, the 19th term of the sequence is -52.