In an increasing geometric progression of positive terms, the sum of the second and sixth terms is and the product of the third and fifth terms is 49 . Then the sum of the and terms is equal to...

aligned& T_2+T_6=703 \\& ar+ar^5=703 \\& ~T_3 ~T_5=49 \\& ar^2 ar^4=49 \\& a^2 r^6=49 \\& ar^3=+7, a=7r^3 \\& ar(1+r^4)=703 \\& 7r^2(1+r^4)=703, r^2=t \\& 1t(1+t^2)=103 \\& 3 t^2-10 t+3=0 \\& t=3, 13 \\& Increasing G.P. r^2=3, r=3 \\& ~T_4+T_6+T_8 \\& =ar^3+ar^5+ar^7 \\& =ar^3(1+r^2+r^4) \\& =7(1+3+...

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is \frac{70}{3} and the product of the third and fifth terms is 49 . Then the sum of the 4^{{th}{~}},6^{{th}{~}} and 8^{{th}{~}} terms is equal to: Sequence & Series (Mathematics)

In an increasing geometric progression of positive terms, the sum of\n the second and sixth terms is

\frac{70}{3}

and the product of the\n third and fifth terms is 49 . Then the sum of the\n

4^{\text{th}\text{~}},6^{\text{th}\text{~}}

and\n

8^{\text{th}\text{~}}

terms is equal to

The sum of the first n terms of the series (1^{2} + 2.2^{2} + 3^{2} + 2.4^{2} + 5^{2} + 2 . 6^{2} + ..) is (\frac{n(n + 1)^{2}}{2}, when n is even. when n is odd, the sum is

Let a,b be two non-zero real numbers. If p and r are the roots of the equation x^{2} - 8ax + 2a = 0 and q and s are the roots of the equation \end{enumerate} x^{2} + 12bx + 6b = 0, such that \frac{1}{p},\frac{1}{q},\frac{1}{r},\frac{1}{s} are in A.P., then a^{- 1} - b^{- 1} is equal to

Different A.P. are constructed with the first term 100 , the last term 199, and integral common differences. The sum of the common differences of all such A.P. having at least 3 terms and at most 33 terms is

If a_1, a_2, a_n are in A.P. where a_i>0 for all i show that &\frac{1}{\sqrt{a_1}+\sqrt{a_2}}+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+\cdots+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}&=\frac{n-1}{\sqrt{a_1}+\sqrt{a_n}}

If a_{n} = \frac{3}{4} - ( \frac{3}{4} )^{2} + ( \frac{3}{4} )^{3} + ( - 1)^{n - 1}( \frac{3}{4} )^{n} and b_{n} = 1 - a_{n}, then find the least natural number n_{0} such that b_{n} > a_{n}\forall n ? n_{0}

For any odd integer n ? 1,n^{3} - (n - 1)^{3} + + ( - 1)^{n - 1}1^{3} =

Let A_{1},G_{1} and H_{1} denote the arithmetic, geometric and harmonic means . respectively of two distinct positive numbers. For n ? 2 let A_{n - 1} and H_{n - 1} have . arithmetic, geometric and harmonic means as A_{n},G_{n},H_{n} respectively. Which of the following statements is correct?

Number of 4 -digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to

If a_{1},a_{2},a_{3}, are in A.P. such that a_{1} + a_{7} + a_{16} = 40, then the sum of the first 15 terms of this A.P. is

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