find the 137th term for the sequence below

Question

40,47,54,61,68,75,82

Answer 1

To find the 137th term of the sequence \(40, 47, 54, 61, 68, 75, 82\), we start by identifying the pattern in the sequence.

1. Identify the First Term and Common Difference:

   • The first term \(a_1 = 40\).
   • The common difference \(d\) can be found by subtracting the first term from the second term: \[ d = 47 - 40 = 7 \]

2. Write the General Formula: The general formula for the \(n\)-th term of an arithmetic sequence is given by: \[ a_n = a_1 + (n - 1) \cdot d \]

3. Substitute Values:

   • For \(n = 137\): \[ a_{137} = 40 + (137 - 1) \cdot 7 \] \[ a_{137} = 40 + 136 \cdot 7 \] \[ a_{137} = 40 + 952 \] \[ a_{137} = 992 \]

Therefore, the 137th term of the sequence is \(\boxed{992}\).