9. Sequences, Series, & Induction

Arithmetic Sequences

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Multiple Choice

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 of the arithmetic sequence, which is $ a_1 = -9 $.

Determine the common difference $ d $ by subtracting the first term from the second term: $ d = -4 - (-9) = 5 $.

Use the general formula for the nth term of an arithmetic sequence: $ a_n = a_1 + (n-1) \cdot d $.

Substitute the known values into the formula to find the 30th term: $ a_{30} = -9 + (30-1) \cdot 5 $.

Simplify the expression to calculate the 30th term: $ a_{30} = -9 + 29 \cdot 5 $.

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Expert video explanations

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,…}