Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the $30^{\th}$ term.
$\left\lbrace-9,-4,1,6,\ldots\right\rbrace$

136

146

150

Verified step by step guidance

Identify the first term (a₁) of the arithmetic sequence. In this case, the first term is -9.

Determine the common difference (d) by subtracting the first term from the second term. For this sequence, d = (-4) - (-9) = 5.

Write the general formula for the nth term of an arithmetic sequence: aₙ = a₁ + (n - 1) * d. Substitute the values of a₁ = -9 and d = 5 into the formula.

Simplify the formula to get the explicit expression for the nth term: aₙ = -9 + (n - 1) * 5.

To find the 30th term (a₃₀), substitute n = 30 into the formula: a₃₀ = -9 + (30 - 1) * 5. Simplify the expression to calculate the value of the 30th term.

8:22m

Watch next

Master Introduction to Sequences with a bite sized video explanation from Patrick

Sequences practice set

Problem sets built by lead tutors

Expert video explanations

Struggling with Calculus?

Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the 30th30^{\th}30th term.{−9,−4,1,6,…}\left\lbrace-9,-4,1,6,\ldots\right\rbrace{−9,−4,1,6,…}

Watch next

Sequences practice set

Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the $30^{\th}$ term.
$\left\lbrace-9,-4,1,6,\ldots\right\rbrace$