Question

Find the 52nd term. -23, -223, -423, -623,…

Answer 1

In order to find the 52nd term of this sequence, first let's find the common difference.

The common difference can be calculated by subtracting one term by the term before.

Using the second and the first term, we have:

`\begin{gathered} d=-223-(-23) \\ d=-223+23 \\ d=-200 \end{gathered}`

Now, to find the 52nd term, let's use the formula below:

`a_n=a_1+(n-1)d`

For n = 52, we have:

`\begin{gathered} a_(52)=a_1+(52-1)\cdot(-200) \\ a_(52)=-23+51\cdot(-200) \\ a_(52)=-23-10200 \\ a_(52)=-10223 \end{gathered}`

Therefore the 52nd term is -10223.