Question

Use the explicit formula a(n)=a(1)+(n-1)•d to find the 350th term of the sequence below
57, 66, 75, 84, 93,…

a1=__
n=__
d=__

What is the 350th term?

Answer 1

To find the 350th term of the given arithmetic sequence, we start by identifying the first term \( a(1) \) and the common difference \( d \).

1. **Finding \( a(1) \)**:
This is the first term of the sequence. From the sequence provided:
\[
a(1) = 57
\]

2. **Finding \( d \)**:
The common difference \( d \) can be found by subtracting the first term from the second term:
\[
d = a(2) - a(1) = 66 - 57 = 9
\]

3. **Finding \( n \)**:
We need to find the 350th term, so:
\[
n = 350
\]

Now we can use the explicit formula for the \( n \)-th term of an arithmetic sequence:
\[
a(n) = a(1) + (n - 1) \cdot d
\]

Substituting in the values we found:
\[
a(350) = 57 + (350 - 1) \cdot 9
\]

Calculating the expression step-by-step:
\[
a(350) = 57 + (349) \cdot 9
\]
Calculate \( 349 \cdot 9 \):
\[
349 \cdot 9 = 3141
\]
Now, add this to 57:
\[
a(350) = 57 + 3141 = 3198
\]

Thus, the 350th term of the sequence is:
\[
\boxed{3198}
\]

### Summary:
- \( a(1) = 57 \)
- \( n = 350 \)
- \( d = 9 \)
- The 350th term is \( 3198 \)