Which term of the sequence 3, 10, 17, ........... is 136?

Answer

To find which term of the sequence 3, 10, 17, ... is equal to 136, we can follow these steps:

### Step 1: Identify the first term and the common difference
The first term \( a \) of the sequence is 3. To find the common difference \( d \), we can subtract the first term from the second term:
\[ d = a_2 - a_1 = 10 - 3 = 7 \]

### Step 2: Write the formula for the nth term of the arithmetic sequence
The formula for the nth term \( a_n \) of an arithmetic sequence is given by:
\[ a_n = a + (n - 1) \cdot d \]
Substituting the values of \( a \) and \( d \):
\[ a_n = 3 + (n - 1) \cdot 7 \]

### Step 3: Set the nth term equal to 136
We need to find \( n \) such that:
\[ a_n = 136 \]
So we set up the equation:
\[ 3 + (n - 1) \cdot 7 = 136 \]

### Step 4: Solve for \( n \)
First, we will isolate the term involving \( n \):
\[ (n - 1) \cdot 7 = 136 - 3 \]
\[ (n - 1) \cdot 7 = 133 \]
Now, divide both sides by 7:
\[ n - 1 = \frac{133}{7} \]
Calculating \( \frac{133}{7} \):
\[ n - 1 = 19 \]
Now, add 1 to both sides to find \( n \):
\[ n = 19 + 1 = 20 \]

### Conclusion
Thus, the term of the sequence that is equal to 136 is the **20th term**.