Question 1: Find the . between:

Answer:

.

Question 2: Insert between

Answer:

be the 4 A.M.s between

Therefore

Therefore the 4 A.M.s between are

Question 3: Insert between

Answer:

be the 7 A.M.s between

Therefore

Therefore the 4 A.M.s between are

Question 4: Insert between

Answer:

be the 6 A.M.s between

Therefore

Therefore the 6 A.M.s between are

Question 5: There are between . The ratio of the last mean to the first mean is . Find the value of

Answer:

Question 6: Insert , between in such a way that . Find the number of

Answer:

Therefore there are

Question 7: If are inserted between two numbers, prove that the sum of the mean equidistant from the beginning and the end is constant.

Answer:

which is constant.

Question 8: If , then prove that the

Answer:

Now,

And

. Hence proved.

Question 9: Insert five numbers between such that the resulting sequence is an A.P..

Answer:

be the 5 A.M.s between

Therefore

Therefore the 5 A.M.s between are