IDNStudy.com, ang komunidad ng pagbabahagi ng kaalaman. Magtanong ng anumang bagay at makatanggap ng kumpleto at eksaktong sagot mula sa aming komunidad ng mga propesyonal.
Answer:
To insert three arithmetic means between 3 and 11, you can follow these steps:
1. Let the three arithmetic means be \( a_1 \), \( a_2 \), and \( a_3 \).
2. The sequence will be: 3, \( a_1 \), \( a_2 \), \( a_3 \), 11.
3. In an arithmetic sequence, the difference between consecutive terms is constant.
Let the common difference be \( d \).
Then:
\[
a_1 = 3 + d
\]
\[
a_2 = 3 + 2d
\]
\[
a_3 = 3 + 3d
\]
\[
11 = 3 + 4d
\]
Now, solve for \( d \):
\[
11 - 3 = 4d
\]
\[
8 = 4d
\]
\[
d = 2
\]
So, the arithmetic means are:
\[
a_1 = 3 + 2 = 5
\]
\[
a_2 = 3 + 4 = 7
\]
\[
a_3 = 3 + 6 = 9
\]
The three arithmetic means between 3 and 11 are 5, 7, and 9.