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Find the 73 rd term of the arithmetic sequence -28,-34,-40,dots Answer:

Find the 7373 rd term of the arithmetic sequence −28,−34,−40,… -28,-34,-40, \ldots \newlineAnswer:

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Full solution

Q. Find the 7373 rd term of the arithmetic sequence −28,−34,−40,… -28,-34,-40, \ldots \newlineAnswer:
  1. Identify pattern: Identify the pattern of the sequence to determine if it is arithmetic.\newlineThe sequence is decreasing by 66 each time, which means it is an arithmetic sequence with a common difference (dd) of −6-6.
  2. Find first term: Find the first term a1a_1 of the sequence.\newlineThe first term of the sequence is given as −28-28.
  3. Use formula: Use the formula for the nnth term of an arithmetic sequence: an=a1+(n−1)da_n = a_1 + (n - 1)d. We need to find the 7373rd term (a73a_{73}), so n=73n = 73, a1=−28a_1 = -28, and d=−6d = -6.
  4. Calculate 7373rd term: Substitute the values into the formula and calculate the 73rd73^{rd} term.\newlinea73=−28+(73−1)(−6)a_{73} = -28 + (73 - 1)(-6)\newlinea73=−28+(72)(−6)a_{73} = -28 + (72)(-6)\newlinea73=−28−432a_{73} = -28 - 432\newlinea73=−460a_{73} = -460

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