Detdrmine if the sequence is arithm 1) $$ 35,32,29,26, \ldots $$,

Question

UpStudy AI · Accepted Answer

Yes, the sequence $$35, 32, 29, 26, \ldots$$ is an **arithmetic sequence**.

An **arithmetic sequence** is a sequence of numbers in which the difference between consecutive terms is constant. This constant is known as the **common difference**.

Let's analyze the given sequence:

1. **First term ($$a_1$$)**: 35
2. **Second term ($$a_2$$)**: 32
3. **Third term ($$a_3$$)**: 29
4. **Fourth term ($$a_4$$)**: 26
5. **And so on...**

**Calculating the differences between consecutive terms:**

$$
\begin{align*}
a_2 - a_1 &= 32 - 35 = -3 \
a_3 - a_2 &= 29 - 32 = -3 \
a_4 - a_3 &= 26 - 29 = -3 \
&\vdots \
\end{align*}
$$

Since the difference between each pair of consecutive terms is consistently $$-3$$, the common difference ($$d$$) is $$-3$$.

**General Formula for the $$n^{th}$$ Term of an Arithmetic Sequence:**

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

Plugging in the known values:

$$
a_n = 35 + (n - 1)(-3) = 35 - 3(n - 1) = 38 - 3n
$$

**Conclusion:**

The sequence $$35, 32, 29, 26, \ldots$$ is indeed an arithmetic sequence with a common difference of $$-3$$.
The sequence $$35, 32, 29, 26, \ldots$$ is an arithmetic sequence with a common difference of $$-3$$.

Detdrmine if the sequence is arithm 1) \( 35,32,29,26, \ldots \),

Solución de tutoría real

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Arithmetic Questions