To insert three arithmetic means between 11 and 35, we need to find a sequence with five terms where 11 is the first term, 35 is the fifth term, and the three arithmetic means are the second, third, and fourth terms.

Let's denote the sequence as $a_1, a_2, a_3, a_4, a_5$, where:

• $a_1 = 11$
• $a_5 = 35$

The common difference $d$ between consecutive terms in an arithmetic sequence can be found using the formula:

$d = \frac{a_5 - a_1}{4}$

Substituting the values:

$d = \frac{35 - 11}{4} = \frac{24}{4} = 6$

Now we can find the three arithmetic means:

1. Second term ( $a_2$ ): $a_2 = a_1 + d = 11 + 6 = 17$

2. Third term ( $a_3$ ): $a_3 = a_2 + d = 17 + 6 = 23$

3. Fourth term ( $a_4$ ): $a_4 = a_3 + d = 23 + 6 = 29$

So, the three arithmetic means between 11 and 35 are 17, 23, and 29.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. How would you find four arithmetic means between 8 and 32?
2. What is the common difference if three arithmetic means are inserted between 5 and 29?
3. How do you find the sum of an arithmetic sequence?
4. Can you find two arithmetic means between 12 and 36?
5. How does the common difference affect the spacing of terms in an arithmetic sequence?

Tip: The common difference in an arithmetic sequence is constant, meaning each term is equally spaced from the previous one.