Question

find the 87th term of the arithmetic sequence 1, 14, 27, ...

Explanation:

Step1: Identify the first term and common difference

For an arithmetic sequence, the first term \(a_1 = 1\). The common difference \(d\) is found by subtracting the first term from the second term: \(d=14 - 1=13\).

Step2: Use the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\). We want to find the 87th term, so \(n = 87\), \(a_1 = 1\), and \(d = 13\). Substitute these values into the formula:
\(a_{87}=1+(87 - 1)\times13\)

Step3: Simplify the expression

First, calculate \(87 - 1 = 86\). Then, multiply \(86\times13\): \(86\times13 = 1118\). Finally, add 1: \(a_{87}=1 + 1118=1119\).

Answer:

1119