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Find the 100 th term of the arithmetic sequence 18,31,44,dots Answer:

Find the 100100 th term of the arithmetic sequence 18,31,44,… 18,31,44, \ldots \newlineAnswer:

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Full solution

Q. Find the 100100 th term of the arithmetic sequence 18,31,44,… 18,31,44, \ldots \newlineAnswer:
  1. Identify Common Difference: Identify the common difference in the arithmetic sequence.\newlineTo find the common difference, subtract the first term from the second term.\newline31−18=1331 - 18 = 13\newlineCommon Difference: 1313
  2. Use Formula for nth Term: Use the formula for the nth term of an arithmetic sequence.\newlineThe formula is an=a1+(n−1)da_n = a_1 + (n - 1)d, where ana_n is the nth term, a1a_1 is the first term, nn is the term number, and dd is the common difference.
  3. Substitute Values: Substitute the known values into the formula to find the 100th100^{\text{th}} term.a100=18+(100−1)×13a_{100} = 18 + (100 - 1) \times 13
  4. Perform Calculations: Perform the calculations.\newlinea100=18+(99×13)a_{100} = 18 + (99 \times 13)\newlinea100=18+1287a_{100} = 18 + 1287\newlinea100=1305a_{100} = 1305

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