Exercise 1

(i) Find the sum of first

    \[51\]

terms of the A.P. whose second and third terms are

    \[14\]

and

    \[18\]

, respectively. (ii) The

    \[{{4}^{th}}\]

term of A.P is

    \[22\]

and

    \[{{15}^{th}}\]

term is

    \[66\]

. Find the first term and the common difference. Hence, find the sum of first 8 term of the A.P.

From the question it is given that, \[{{T}_{2}}~=\text{ }14,\text{ }{{T}_{3}}~=\text{ }18\] So, common difference d = \[{{T}_{3}}~\text{ }{{T}_{2}}\] \[\begin{array}{*{35}{l}} =\text{ }18\text{...

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(i) The first term of an A.P. is 5, the last term is

    \[45\]

and the sum is

    \[400\]

. Find the number of terms and the common difference. (ii) The sum of first

    \[15\]

terms of an A.P. is

    \[750\]

and its first term is

    \[15\]

. Find its

    \[20\]

th term.

From the question it is give that, First term a = \[5\] Last term = \[45\] Then, sum = \[400\] We know that, last term = a + (n – 1)d \[\begin{array}{*{35}{l}} 45\text{ }=\text{ }5\text{ }+\text{...

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(i) The

    \[{{15}^{th}}\]

term of an A.P. is

    \[3\]

more than twice its

    \[{{7}^{th}}\]

term. If the

    \[{{10}^{th}}\]

term of the A.P. is

    \[41\]

, find its nth term. (ii) The sum of

    \[{{5}^{th}}\]

and

    \[{{7}^{th}}\]

terms of an A.P. is

    \[52\]

and the

    \[{{10}^{th}}\]

term is

    \[46\]

. Find the A.P.

From the question it I s given that, \[{{T}_{10}}~=\text{ }41\] \[{{T}_{10}}~=\text{ }a\text{ }+\text{ }9d\text{ }=\text{ }41\]… [equation (i)] \[\begin{array}{*{35}{l}} {{T}_{15}}~=\text{ }a\text{...

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(i)If the common difference of an A.P. is

    \[-3\]

and the

    \[\mathbf{1}{{\mathbf{8}}^{\mathbf{th}}}\]

term is

    \[-5\]

, then find its first term. (ii) If the first term of an A.P. is

    \[-18\]

and its

    \[10\]

th term is zero, then find its common difference.

From the question it is given that, The \[\mathbf{1}{{\mathbf{8}}^{\mathbf{th}}}\] term = \[-5\] Then, common difference d = \[-3\] \[\begin{array}{*{35}{l}} {{T}_{n}}~=\text{ }a\text{ }+\text{...

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