Find the indacted term for the arithmetic sequence with a first term $$ a 1 $$, and a common differnce of $$ d $$ find $$ a 16 $$ when $$ a=1, d=2 $$

Question

UpStudy AI · Accepted Answer

In an arithmetic sequence, the $$ n $$-th term can be calculated using the formula:

$$
a_n = a_1 + (n - 1) \cdot d
$$

where:
- $$ a_n $$ is the $$ n $$-th term,
- $$ a_1 $$ is the first term,
- $$ d $$ is the common difference,
- $$ n $$ is the term number.

Given:
- $$ a_1 = 1 $$
- $$ d = 2 $$
- $$ n = 16 $$

We can substitute these values into the formula to find $$ a_{16} $$:

$$
a_{16} = 1 + (16 - 1) \cdot 2
$$

Calculating the expression inside the parentheses:

$$
16 - 1 = 15
$$

Now, substituting back into the equation:

$$
a_{16} = 1 + 15 \cdot 2
$$

Calculating $$ 15 \cdot 2 $$:

$$
15 \cdot 2 = 30
$$

Now, adding this to 1:

$$
a_{16} = 1 + 30 = 31
$$

Thus, the 16th term $$ a_{16} $$ is:

$$
\boxed{31}
$$
$$ a_{16} = 31 $$

Find the indacted term for the arithmetic sequence with a first term \( a 1 \), and a common differnce of \( d \) find \( a 16 \) when \( a=1, d=2 \)