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In Math / Senior High School | 2024-09-05

what is the value of 30th term of the sequence 22,18,14​

Asked by romulocabuhat218

Answer (2)

SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & n = 30 \\ & a_1 = 22 \\ & a_2 = 18 \\ & a_3 = 14 \end{aligned}[/tex]Step 2: Find the common difference.[tex]\begin{aligned} d & = a_2 - a_1 = a_3 - a_2 \\ & = 18 - 22 = 14 - 18 \\ d & = -4 = -4 \end{aligned}[/tex]Step 3: Solve for the 30th term of an arithmetic sequence.[tex]\begin{aligned} a_n & = a_1 + (n - 1)d \\ a_{30} & = 22 + (30 - 1)(-4) \\ & = 22 + 29(-4) \\ & = 22 - 116 \\ & = \boxed{-94} \end{aligned}[/tex]Hence, the 30th term of an arithmetic sequence is -94.

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