Question

Find the 52nd term of the given arithmetic sequence-30, -38, -46, -54...

Answer 1

The sequence is given to be:

`-30,-38,-46,-54...`

The nth term of an arithmetic sequence is calculated using the formula:

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

where a₁ is the first term, n is the number of terms, and d is the common difference.

From the given sequence, the following parameters can be gotten:

`\begin{gathered} a_1=-30 \\ d=-38-(-30)=-8 \end{gathered}`

Therefore, the parameters can be substituted into the formula to find the 52nd term:

`\begin{gathered} n=52 \\ \therefore \\ a_(52)=-30+(52-1)(-8) \\ a_(52)=-30+51(-8)=-30-408 \\ a_(52)=-438 \end{gathered}`

The 52nd term is -438.