Question

find the 137th term for the sequence below
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 \(\boxed{992}\).