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Find the 63 rd term of the arithmetic sequence -17,-11,-5,dots Answer:

Find the 6363 rd term of the arithmetic sequence −17,−11,−5,… -17,-11,-5, \ldots \newlineAnswer:

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Full solution

Q. Find the 6363 rd term of the arithmetic sequence −17,−11,−5,… -17,-11,-5, \ldots \newlineAnswer:
  1. Identify common difference: Identify the common difference in the arithmetic sequence.\newlineThe sequence is −17-17, −11-11, −5-5, ... To find the common difference, subtract the first term from the second term.\newlineCommon difference (d)=−11−(−17)=−11+17=6(d) = -11 - (-17) = -11 + 17 = 6
  2. Use formula for nth term: Use the formula for the nth term of an arithmetic sequence.\newlineThe nth term ana_n of an arithmetic sequence can be found using the formula:\newlinean=a1+(n−1)⋅da_n = a_1 + (n - 1) \cdot d\newlinewhere a1a_1 is the first term, nn is the term number, and dd is the common difference.
  3. Plug values for 6363rd term: Plug the values into the formula to find the 63rd63^{\text{rd}} term.\newlinea1=−17a_1 = -17 (the first term)\newlinen=63n = 63 (the term number we are looking for)\newlined=6d = 6 (the common difference)\newlineNow, calculate the 63rd63^{\text{rd}} term:\newlinea63=−17+(63−1)×6a_{63} = -17 + (63 - 1) \times 6
  4. Perform calculations: Perform the calculations.\newlinea63=−17+(62×6)a_{63} = -17 + (62 \times 6)\newlinea63=−17+372a_{63} = -17 + 372\newlinea63=355a_{63} = 355

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