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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.\newline15,30,45,60,…15, 30, 45, 60, \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.\newline15,30,45,60,…15, 30, 45, 60, \ldots\newlinean=a_n = _____
  1. Sequence Type: We have the sequence: 15,30,45,60,…15, 30, 45, 60, \ldots\newlineIs the given sequence geometric or arithmetic?\newline15,30,45,60,…15, 30, 45, 60, \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=15a_1 = 15\newlineCommon difference, d=30−15=15d = 30 - 15 = 15
  3. Arithmetic Sequence Formula: We have the formula for the nth term of an arithmetic sequence:\newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlinea1=15a_1 = 15\newlined=15d = 15\newlineWrite an expression to describe 1515, 3030, 4545, 6060, ...\newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlinean=15+(n−1)×15a_n = 15 + (n-1) \times 15\newlinean=15+15n−15a_n = 15 + 15n - 15\newlinean=15na_n = 15n

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