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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.\newline–39,–78,–117,–156,…\text{–}39, \text{–}78, \text{–}117, \text{–}156, \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.\newline–39,–78,–117,–156,…\text{–}39, \text{–}78, \text{–}117, \text{–}156, \ldots\newlinean=a_n = _____
  1. Identify sequence type: Identify the type of sequence.\newlineWe have: −39-39, −78-78, −117-117, −156-156, ...\newlineIs the given sequence geometric or arithmetic?\newline−39-39, −78-78, −117-117, −156-156, ...\newlineHere, there is a common difference between consecutive terms.\newlineThe given sequence is arithmetic.
  2. Determine values of a1a_1 and dd: Determine the values of a1a_1 and dd of the sequence. The first term, a1=−39a_1 = -39 Common difference, d=−78−(−39)=−39d = -78 - (-39) = -39
  3. Write nth term formula: Write the formula for the nth term of an arithmetic sequence.\newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlinea1=−39a_1 = -39\newlined=−39d = -39\newlineWrite an expression to describe −39,−78,−117,−156,...-39, -78, -117, -156, ...\newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlinean=−39+(n−1)(−39)a_n = -39 + (n-1)(-39)
  4. Simplify expression: Simplify the expression.\newlinean=−39+(−39n+39)a_{n} = -39 + (-39n + 39)\newlinean=−39n+39−39a_{n} = -39n + 39 - 39\newlinean=−39na_{n} = -39n

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