Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. –83, –166, –249, –332, ... an = _____

Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.  –83, –166, –249, –332, ...  an = _____

Bytelearn · Accepted Answer

Identify type of sequence: Identify the type of sequence. We have:  –83, –166, –249, –332, ...  Is the given sequence geometric or arithmetic?  To determine this, we look at the differences between consecutive terms. –166 - (–83) = –83 –249 - (–166) = –83 –332 - (–249) = –83 Since there is a common difference between consecutive terms, the given sequence is arithmetic.Determine values of a1 and d: Determine the values of a1 and d of the sequence. The first term, a1 = –83 Common difference, d = –166 - (–83) = –83Write nth term formula: Write the formula for the nth term of an arithmetic sequence. The formula for the nth term of an arithmetic sequence is: an = a1 + (n-1)dSubstitute values into formula: Substitute the values of a1 and d into the formula. a1 = –83 d = –83 an = a1 + (n-1)d an = –83 + (n-1)(–83)Simplify expression: Simplify the expression. an = –83 - 83(n-1) an = –83 - 83n + 83 an = –83n Since –83 + 83 equals 0, the simplified expression is: an = –83n

Write an expression to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n = 1$ for the first term. $\newline$ $–83, –166, –249, –332, \dots$ $\newline$ $a_n =$ _____

Full solution

More problems from Write variable expressions for arithmetic sequences

Related topics

Write an expression to describe the sequence below. Use nnn to represent the position of a term in the sequence, where n=1n = 1n=1 for the first term.\newline–83,–166,–249,–332,…–83, –166, –249, –332, \dots–83,–166,–249,–332,…\newlinean=a_n = an​=_____

Write an expression to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n = 1$ for the first term. $\newline$ $–83, –166, –249, –332, \dots$ $\newline$ $a_n =$ _____