Geometric Progression
Sequence and Series

118677 Let the H.M. and G.M. of two positive numbers \(a\) and \(b\) be in the ratio \(4: 5\), then \(a: b\) is

1 \(1: 2\)
2 \(2: 3\)
3 \(3: 4\)
4 \(1: 4\)
Sequence and Series

118678 The sum of the A.M. and G.M. of two positive numbers is equal to the difference between the numbers. The numbers are in the ratio

1 \(1: 3\)
2 \(1: 6\)
3 \(9: 1\)
4 \(1: 12\)
Sequence and Series

118679 A group of 10 items has arithmetic mean 6 . If the arithmetic mean of 4 of these items is 7.5 , then the mean of the remaining items is

1 6.5
2 5.5
3 4.5
4 5.0
Sequence and Series

118681 Let \(x_1, x_2, \ldots, x_n\) be \(n\) observations such that \(\sum x_i^2=400, \sum x_i=80\). Then the possible value of \(n\) is

1 15
2 18
3 9
4 12
Sequence and Series

118682 If \(m\) arithmetic mean are inserted between 1 and 31 so that the ratio of the \(7^{\text {th }}\) and \((m-1)^{\text {th }}\) means is \(5: 9\), then find the value of \(m\).

1 14
2 24
3 10
4 20
Sequence and Series

118677 Let the H.M. and G.M. of two positive numbers \(a\) and \(b\) be in the ratio \(4: 5\), then \(a: b\) is

1 \(1: 2\)
2 \(2: 3\)
3 \(3: 4\)
4 \(1: 4\)
Sequence and Series

118678 The sum of the A.M. and G.M. of two positive numbers is equal to the difference between the numbers. The numbers are in the ratio

1 \(1: 3\)
2 \(1: 6\)
3 \(9: 1\)
4 \(1: 12\)
Sequence and Series

118679 A group of 10 items has arithmetic mean 6 . If the arithmetic mean of 4 of these items is 7.5 , then the mean of the remaining items is

1 6.5
2 5.5
3 4.5
4 5.0
Sequence and Series

118681 Let \(x_1, x_2, \ldots, x_n\) be \(n\) observations such that \(\sum x_i^2=400, \sum x_i=80\). Then the possible value of \(n\) is

1 15
2 18
3 9
4 12
Sequence and Series

118682 If \(m\) arithmetic mean are inserted between 1 and 31 so that the ratio of the \(7^{\text {th }}\) and \((m-1)^{\text {th }}\) means is \(5: 9\), then find the value of \(m\).

1 14
2 24
3 10
4 20
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Sequence and Series

118677 Let the H.M. and G.M. of two positive numbers \(a\) and \(b\) be in the ratio \(4: 5\), then \(a: b\) is

1 \(1: 2\)
2 \(2: 3\)
3 \(3: 4\)
4 \(1: 4\)
Sequence and Series

118678 The sum of the A.M. and G.M. of two positive numbers is equal to the difference between the numbers. The numbers are in the ratio

1 \(1: 3\)
2 \(1: 6\)
3 \(9: 1\)
4 \(1: 12\)
Sequence and Series

118679 A group of 10 items has arithmetic mean 6 . If the arithmetic mean of 4 of these items is 7.5 , then the mean of the remaining items is

1 6.5
2 5.5
3 4.5
4 5.0
Sequence and Series

118681 Let \(x_1, x_2, \ldots, x_n\) be \(n\) observations such that \(\sum x_i^2=400, \sum x_i=80\). Then the possible value of \(n\) is

1 15
2 18
3 9
4 12
Sequence and Series

118682 If \(m\) arithmetic mean are inserted between 1 and 31 so that the ratio of the \(7^{\text {th }}\) and \((m-1)^{\text {th }}\) means is \(5: 9\), then find the value of \(m\).

1 14
2 24
3 10
4 20
Sequence and Series

118677 Let the H.M. and G.M. of two positive numbers \(a\) and \(b\) be in the ratio \(4: 5\), then \(a: b\) is

1 \(1: 2\)
2 \(2: 3\)
3 \(3: 4\)
4 \(1: 4\)
Sequence and Series

118678 The sum of the A.M. and G.M. of two positive numbers is equal to the difference between the numbers. The numbers are in the ratio

1 \(1: 3\)
2 \(1: 6\)
3 \(9: 1\)
4 \(1: 12\)
Sequence and Series

118679 A group of 10 items has arithmetic mean 6 . If the arithmetic mean of 4 of these items is 7.5 , then the mean of the remaining items is

1 6.5
2 5.5
3 4.5
4 5.0
Sequence and Series

118681 Let \(x_1, x_2, \ldots, x_n\) be \(n\) observations such that \(\sum x_i^2=400, \sum x_i=80\). Then the possible value of \(n\) is

1 15
2 18
3 9
4 12
Sequence and Series

118682 If \(m\) arithmetic mean are inserted between 1 and 31 so that the ratio of the \(7^{\text {th }}\) and \((m-1)^{\text {th }}\) means is \(5: 9\), then find the value of \(m\).

1 14
2 24
3 10
4 20
Sequence and Series

118677 Let the H.M. and G.M. of two positive numbers \(a\) and \(b\) be in the ratio \(4: 5\), then \(a: b\) is

1 \(1: 2\)
2 \(2: 3\)
3 \(3: 4\)
4 \(1: 4\)
Sequence and Series

118678 The sum of the A.M. and G.M. of two positive numbers is equal to the difference between the numbers. The numbers are in the ratio

1 \(1: 3\)
2 \(1: 6\)
3 \(9: 1\)
4 \(1: 12\)
Sequence and Series

118679 A group of 10 items has arithmetic mean 6 . If the arithmetic mean of 4 of these items is 7.5 , then the mean of the remaining items is

1 6.5
2 5.5
3 4.5
4 5.0
Sequence and Series

118681 Let \(x_1, x_2, \ldots, x_n\) be \(n\) observations such that \(\sum x_i^2=400, \sum x_i=80\). Then the possible value of \(n\) is

1 15
2 18
3 9
4 12
Sequence and Series

118682 If \(m\) arithmetic mean are inserted between 1 and 31 so that the ratio of the \(7^{\text {th }}\) and \((m-1)^{\text {th }}\) means is \(5: 9\), then find the value of \(m\).

1 14
2 24
3 10
4 20