118680 The arithmetic mean of the series \(1,2,4,8\), \(16, \ldots . ., 2^{\mathrm{n}}\) is
#[Qdiff: Very Easy, QCat: Theory Based, examname: SRM JEEE-2011]\(\therefore \text { Required mean }=\frac{1+2+4+8+\ldots .+2^{\mathrm{n}}}{\mathrm{n}+1}\)
, \(=\frac{2^0+2^1+2^2+\ldots \ldots+2^{\mathrm{n}}}{\mathrm{n}+1}\)
, \(=\frac{1\left(\frac{2^{n+1}-1}{2-1}\right)}{n+1}\)
, \({\left[\because 2^0, 2^1, 2^2, \ldots \ldots 2^{\text {n }} \text { is a G.P. }\right]}\)
, \(=\frac{2^{n+1}-1}{n+1}\)]#

118673 If the 9th term of an AP is zero, then the ratio of 29 th term to 19 th term is

118665 A arithmetic mean progression of two numbers is 6 more than the geometric mean progression of the numbers. The ratio of number is \(9: 1\), then numbers are

118666 If \(a, b\) and \(c\) are in HP, then for any \(n \in N\), which one of the following is true?

118667 If the sum of four numbers in GP is 60 and the arithmetic mean of the first and last numbers is 18 , then the numbers are

118680 The arithmetic mean of the series \(1,2,4,8\), \(16, \ldots . ., 2^{\mathrm{n}}\) is
#[Qdiff: Very Easy, QCat: Theory Based, examname: SRM JEEE-2011]\(\therefore \text { Required mean }=\frac{1+2+4+8+\ldots .+2^{\mathrm{n}}}{\mathrm{n}+1}\)
, \(=\frac{2^0+2^1+2^2+\ldots \ldots+2^{\mathrm{n}}}{\mathrm{n}+1}\)
, \(=\frac{1\left(\frac{2^{n+1}-1}{2-1}\right)}{n+1}\)
, \({\left[\because 2^0, 2^1, 2^2, \ldots \ldots 2^{\text {n }} \text { is a G.P. }\right]}\)
, \(=\frac{2^{n+1}-1}{n+1}\)]#

118673 If the 9th term of an AP is zero, then the ratio of 29 th term to 19 th term is

118665 A arithmetic mean progression of two numbers is 6 more than the geometric mean progression of the numbers. The ratio of number is \(9: 1\), then numbers are

118666 If \(a, b\) and \(c\) are in HP, then for any \(n \in N\), which one of the following is true?

118667 If the sum of four numbers in GP is 60 and the arithmetic mean of the first and last numbers is 18 , then the numbers are

118680 The arithmetic mean of the series \(1,2,4,8\), \(16, \ldots . ., 2^{\mathrm{n}}\) is
#[Qdiff: Very Easy, QCat: Theory Based, examname: SRM JEEE-2011]\(\therefore \text { Required mean }=\frac{1+2+4+8+\ldots .+2^{\mathrm{n}}}{\mathrm{n}+1}\)
, \(=\frac{2^0+2^1+2^2+\ldots \ldots+2^{\mathrm{n}}}{\mathrm{n}+1}\)
, \(=\frac{1\left(\frac{2^{n+1}-1}{2-1}\right)}{n+1}\)
, \({\left[\because 2^0, 2^1, 2^2, \ldots \ldots 2^{\text {n }} \text { is a G.P. }\right]}\)
, \(=\frac{2^{n+1}-1}{n+1}\)]#

118673 If the 9th term of an AP is zero, then the ratio of 29 th term to 19 th term is

118665 A arithmetic mean progression of two numbers is 6 more than the geometric mean progression of the numbers. The ratio of number is \(9: 1\), then numbers are

118666 If \(a, b\) and \(c\) are in HP, then for any \(n \in N\), which one of the following is true?

118667 If the sum of four numbers in GP is 60 and the arithmetic mean of the first and last numbers is 18 , then the numbers are

118680 The arithmetic mean of the series \(1,2,4,8\), \(16, \ldots . ., 2^{\mathrm{n}}\) is
#[Qdiff: Very Easy, QCat: Theory Based, examname: SRM JEEE-2011]\(\therefore \text { Required mean }=\frac{1+2+4+8+\ldots .+2^{\mathrm{n}}}{\mathrm{n}+1}\)
, \(=\frac{2^0+2^1+2^2+\ldots \ldots+2^{\mathrm{n}}}{\mathrm{n}+1}\)
, \(=\frac{1\left(\frac{2^{n+1}-1}{2-1}\right)}{n+1}\)
, \({\left[\because 2^0, 2^1, 2^2, \ldots \ldots 2^{\text {n }} \text { is a G.P. }\right]}\)
, \(=\frac{2^{n+1}-1}{n+1}\)]#

118673 If the 9th term of an AP is zero, then the ratio of 29 th term to 19 th term is

118665 A arithmetic mean progression of two numbers is 6 more than the geometric mean progression of the numbers. The ratio of number is \(9: 1\), then numbers are

118666 If \(a, b\) and \(c\) are in HP, then for any \(n \in N\), which one of the following is true?

118667 If the sum of four numbers in GP is 60 and the arithmetic mean of the first and last numbers is 18 , then the numbers are

118680 The arithmetic mean of the series \(1,2,4,8\), \(16, \ldots . ., 2^{\mathrm{n}}\) is
#[Qdiff: Very Easy, QCat: Theory Based, examname: SRM JEEE-2011]\(\therefore \text { Required mean }=\frac{1+2+4+8+\ldots .+2^{\mathrm{n}}}{\mathrm{n}+1}\)
, \(=\frac{2^0+2^1+2^2+\ldots \ldots+2^{\mathrm{n}}}{\mathrm{n}+1}\)
, \(=\frac{1\left(\frac{2^{n+1}-1}{2-1}\right)}{n+1}\)
, \({\left[\because 2^0, 2^1, 2^2, \ldots \ldots 2^{\text {n }} \text { is a G.P. }\right]}\)
, \(=\frac{2^{n+1}-1}{n+1}\)]#

118673 If the 9th term of an AP is zero, then the ratio of 29 th term to 19 th term is

118665 A arithmetic mean progression of two numbers is 6 more than the geometric mean progression of the numbers. The ratio of number is \(9: 1\), then numbers are

118666 If \(a, b\) and \(c\) are in HP, then for any \(n \in N\), which one of the following is true?

118667 If the sum of four numbers in GP is 60 and the arithmetic mean of the first and last numbers is 18 , then the numbers are