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In this lesson, we will learn how to find the arithmetic means for any two nonconsecutive terms in an arithmetic sequence.

Q1:

Find π , π , and π given the arithmetic sequence π , 4 4 , π , 6 4 , π .

Q2:

Find the number of the arithmetic means inserted between β 4 and 101 given the twelveth mean is 8 times the second one.

Q3:

Find the number of the arithmetic means inserted between β 8 3 and 169 given the seventeenth mean is 121 times the seventh one.

Q4:

Find the number of the arithmetic means inserted between β 6 6 and 121 given the fifteenth mean is 9 times the seventh one.

Q5:

Find the number of arithmetic means inserted between 2 and 254 given the ratio between the sum of the first two means and the sum of the last two means is 1 1 2 4 5 .

Q6:

Find the number of arithmetic means inserted between 99 and 183 given the ratio between the sum of the first two means and the sum of the last two means is 1 8 2 9 .

Q7:

Find the number of arithmetic means inserted between β 1 5 9 and β 1 5 given the ratio between the sum of the first two means and the sum of the last two means is 4 9 9 .

Q8:

Find the number of arithmetic terms inserted between 2 and 104 given the sum of the fifteenth and twentieth term is 109.

Q9:

Find the number of arithmetic terms inserted between 9 and 387 given the sum of the fifteenth and twentieth term is 333.

Q10:

Find the number of arithmetic terms inserted between 6 and 210 given the sum of the fifteenth and twentieth term is 222.

Q11:

The arithmetic mean between β 4 5 and π is 24. Find π .

Q12:

Find the number of arithmetic means inserted between 194 and 90 given the ratio between the second and the last means is 9 3 4 7 .

Q13:

Find the number of arithmetic means inserted between β 1 3 3 and β 7 7 given the ratio between the second and the last means is 1 2 5 8 1 .

Q14:

Find the number of arithmetic means inserted between 157 and β 1 1 3 given the ratio between the second and the last means is β 1 3 9 1 0 4 .

Q15:

Evaluate the arithmetic mean between β 7 7 and 24.

Q16:

Find the two numbers whose arithmetic mean is 126, given the ratio between them is 1 2 .

Q17:

Find the two numbers whose arithmetic mean is 308.5 and product is 616.

Q18:

If π arithmetic means are inserted between β 1 0 8 and β 5 6 , where the fourth mean exceeds the sum of the two means whose orders are ( π β 2 ) and ( π β 4 ) by 52, determine π .

Q19:

If π arithmetic means are inserted between 166 and β 5 8 , where the fourth mean exceeds the sum of the two means whose orders are ( π β 2 ) and ( π β 4 ) by 114, determine π .

Q20:

If π arithmetic means are inserted between 143 and β 1 6 1 , where the fourth mean exceeds the sum of the two means whose orders are ( π β 2 ) and ( π β 4 ) by 369, determine π .

Q21:

Find the number of arithmetic means inserted between 8 and 238 given the sum of the second and the sixth means is 96.

Q22:

Find the two numbers whose arithmetic mean is 49, where one number is 17 more than twice the other.

Q23:

Insert 5 arithmetic means between 7 and 19.

Q24:

Insert 5 arithmetic means between 10 and 46.

Q25:

Find the last arithmetic mean when 27 means are inserted between β 8 6 and β 5 8 .

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