Arithmetic Means

Insert [3] arithmetic means between - 14 and - 50 ?

• - 24, - 34, - 44

• - 20, - 31, - 42

• - 23, - 32, - 41

• - 21, - 32, - 43

Answer explanation

To find 3 arithmetic means between -14 and -50, calculate the common difference: (-50 - (-14)) / 4 = -9. The means are -14 - 9 = -23, -23 - 9 = -32, -32 - 9 = -41. Thus, the correct answer is -23, -32, -41.

Insert [3] arithmetic means between -37 and -17.

• -32,-27,-22

• -30.-25,-27

• -25,-27,-29

• -20,-24,-26

Answer explanation

To find 3 arithmetic means between -37 and -17, calculate the common difference: (-17 - (-37)) / 4 = 5. The means are -37 + 5, -32 + 5, -27 + 5, resulting in -32, -27, -22. Thus, the correct choice is -32, -27, -22.

Insert [3] arithmetic means between -3, and 37.

• 9, 17, 25

• 11, 21, 31

• 7, 17, 27

• 13, 23, 33

Answer explanation

To find 3 arithmetic means between -3 and 37, calculate the common difference: (37 - (-3)) / 4 = 10. The means are -3 + 10 = 7, 7 + 10 = 17, and 17 + 10 = 27. Thus, the correct answer is 7, 17, 27.

Three arithmetic means are inserted between 9 and 25. What is the first of these arithmetic means?

• 13

• 17

• 19

• 21

Answer explanation

To find the first arithmetic mean between 9 and 25, calculate the common difference. The total difference is 25 - 9 = 16, divided by 4 (the number of intervals) gives 4. Thus, the first mean is 9 + 4 = 13.

Three arithmetic means are inserted between 9 and 25. What is the second of these arithmetic means?

• 13

• 17

• 19

• 21

Answer explanation

To find the arithmetic means, calculate the common difference: (25 - 9) / 4 = 4. The means are 13, 17, 21, and the second mean is 17.

Three arithmetic means are inserted between 9 and 25. What is the third of these arithmetic means?

• 13

• 17

• 19

• 21

Answer explanation

To find the three arithmetic means between 9 and 25, we calculate the common difference: (25 - 9) / 4 = 4. The means are 13, 17, and 21. Thus, the third arithmetic mean is 21.

The arithmetic mean between two terms in an arithmetic sequence is 1. If one term is 5, what is the other term?

• - 7

• - 3

• 4

• 9

Answer explanation

The arithmetic mean of two terms a and b is given by (a + b) / 2. Here, (5 + x) / 2 = 1. Solving for x gives 5 + x = 2, so x = 2 - 5 = -3. Thus, the other term is -3.

There are [6] arithmetic means between a₁ and a₇

• True

• False

Answer explanation

The statement is false because there are 5 arithmetic means between a1 and a7. The number of means is always one less than the number of terms, so with 7 terms (a1 to a7), there are 5 means.

Answer explanation

The arithmetic mean is calculated by averaging the two fractions: \( \frac{1}{4} \) and \( \frac{3}{4} \). Adding them gives \( \frac{1}{4} + \frac{3}{4} = 1 \). Dividing by 2 results in \( \frac{1}{2} \), which is the correct answer.