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Write an expression to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n = 1 for the first term.\newline40,80,120,160,…40, 80, 120, 160, \ldots\newlinean=a_n = _____

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Q. Write an expression to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n = 1 for the first term.\newline40,80,120,160,…40, 80, 120, 160, \ldots\newlinean=a_n = _____
  1. Sequence Type: We have: \newline40,80,120,160,…40, 80, 120, 160, \ldots \newlineIs the given sequence geometric or arithmetic? \newline40,80,120,160,…40, 80, 120, 160, \ldots \newlineHere, there is a common difference between consecutive terms.\newlineThe given sequence is arithmetic.
  2. Find a1a_1 and dd: Determine the values of a1a_1 and dd of the sequence. \newlineThe first term, a1=40a_1 = 40 \newlineCommon difference, d=80−40=40d = 80 - 40 = 40
  3. Expression for Sequence: We have: \newlinean=a1+(n−1)da_n = a_1 + (n-1)d \newlinea1=40a_1 = 40 \newlined=40d = 40 \newlineWrite an expression to describe 4040, 8080, 120120, 160160, ... \newlinean=a1+(n−1)da_n = a_1 + (n-1)d \newlinean=40+(n−1)×40a_n = 40 + (n-1) \times 40 \newlinean=40+40n−40a_n = 40 + 40n - 40 \newlinean=40na_n = 40n

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