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An arithmetic sequence
j starts
22,15,dots. Explain how you would calculate the value of the 500th term.

An arithmetic sequence $j$ starts $22,15, \ldots$ . Explain how you would calculate the value of the $500$ th term.

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Convert between customary and metric systems

Full solution

Q. An arithmetic sequence

j

starts

22,15, \ldots

. Explain how you would calculate the value of the

500

th term.

Find First Term: First term $(a) = 22$ Common difference $(d) = 15 - 22 = -7$
Arithmetic Sequence Formula: Formula for the nth term of an arithmetic sequence: $a_n = a + (n-1)d$
Substitute Values: Substitute n = $500$ , a = $22$ , and d = $-7$ into the formula: $\newline$ $a_{500} = 22 + (500-1)(-7)$
Calculate n $-1$ : Calculate $500-1$ : $\newline$ $499$
Multiply by $-7$ : Multiply $499$ by $-7$ : $\newline$ $499 \times -7 = -3493$
Add to Find Term: Add $22$ to $-3493$ : $\newline$ $22 + (-3493) = -3471$

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