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Find the 84 th term of the arithmetic sequence 23,39,55,dots Answer:

Find the 8484 th term of the arithmetic sequence 23,39,55,… 23,39,55, \ldots \newlineAnswer:

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Full solution

Q. Find the 8484 th term of the arithmetic sequence 23,39,55,… 23,39,55, \ldots \newlineAnswer:
  1. Identify Common Difference: Identify the common difference of the arithmetic sequence.\newlineTo find the common difference, subtract the first term from the second term.\newline39−23=1639 - 23 = 16\newlineCommon Difference: 1616
  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)d\newlinewhere a1a_1 is the first term, dd is the common difference, and nn is the term number.
  3. Calculate 84th84^{\text{th}} Term: Calculate the 84th84^{\text{th}} term using the formula.a1=23a_1 = 23 (first term)d=16d = 16 (common difference)n=84n = 84 (term number)a84=23+(84−1)×16a_{84} = 23 + (84 - 1) \times 16
  4. Perform Calculation: Perform the calculation.\newlinea84=23+(83×16)a_{84} = 23 + (83 \times 16)\newlinea84=23+1328a_{84} = 23 + 1328\newlinea84=1351a_{84} = 1351

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