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.