Login/Sign Up
Home » 1. Find the sum of the following A.P.s : (i)     terms (ii)     terms
1. Find the sum of the following A.P.s : (i)

    \[\mathbf{2},\text{ }\mathbf{7},\text{ }\mathbf{12},\text{ }\ldots \text{ }\mathbf{to}\text{ }\mathbf{10}\]

terms (ii)

    \[\mathbf{1}/\mathbf{15},\text{ }\mathbf{1}/\mathbf{12},\text{ }\mathbf{1}/\mathbf{10},\text{ }\ldots \text{ }\mathbf{to}\text{ }\mathbf{11}\]

terms
Arithmetic and Geometric Progression | Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal
1. Find the sum of the following A.P.s : (i)

    \[\mathbf{2},\text{ }\mathbf{7},\text{ }\mathbf{12},\text{ }\ldots \text{ }\mathbf{to}\text{ }\mathbf{10}\]

terms (ii)

    \[\mathbf{1}/\mathbf{15},\text{ }\mathbf{1}/\mathbf{12},\text{ }\mathbf{1}/\mathbf{10},\text{ }\ldots \text{ }\mathbf{to}\text{ }\mathbf{11}\]

terms

From the question,

First term a =

    \[2\]

Then, d =

    \[7\text{ }\text{ }2\text{ }=\text{ }5\]

    \[12\text{ }\text{ }7\text{ }=\text{ }5\]

So, common difference d =

    \[5\]

    \[\begin{array}{*{35}{l}}</strong> <strong> n\text{ }=\text{ }10 \\</strong> <strong> {{S}_{10}}~=\text{ }n/2\left( 2a\text{ }+\text{ }\left( n\text{ }\text{ }1 \right)d \right) \\</strong> <strong> =\text{ }10/2\text{ }\left( \left( 2\text{ }\times \text{ }2 \right)\text{ }+\text{ }\left( 10\text{ }\text{ }1 \right)5 \right) \\</strong> <strong> =\text{ }5\left( 4\text{ }+\text{ }45 \right) \\</strong> <strong> =\text{ }5\left( 49 \right) \\</strong> <strong> =\text{ }245 \\</strong> <strong>\end{array}\]

(ii)

    \[\mathbf{1}/\mathbf{15},\text{ }\mathbf{1}/\mathbf{12},\text{ }\mathbf{1}/\mathbf{10},\text{ }\ldots \text{ }\mathbf{to}\text{ }\mathbf{11}\]

 terms

Solution:-

From the question,

First term a =

    \[1/15\]

Then, d =

    \[1/12\text{ }\text{ }1/15\]

    \[\begin{array}{*{35}{l}} =\text{ }\left( 5\text{ }\text{ }4 \right)/60 \\ =\text{ }1/60 \\ \end{array}\]

So, common difference d =

    \[1/60\]

n =

    \[11\]

    \[\begin{array}{*{35}{l}}</strong> <strong> {{S}_{11}}~=\text{ }11/2\left( 2a\text{ }+\text{ }\left( n\text{ }\text{ }1 \right)d \right) \\</strong> <strong> =\text{ }11/2\text{ }\left( \left( 2\text{ }\times \text{ }\left( 1/15 \right) \right)\text{ }+\text{ }\left( 11\text{ }\text{ }1 \right)\left( 1/60 \right) \right) \\</strong> <strong> =\text{ }11/2\text{ }\left( \left( 2/15 \right)\text{ }+\text{ }\left( 10/60 \right) \right) \\</strong> <strong> =\text{ }11/2\text{ }\left( 2/15\text{ }+\text{ }1/6 \right) \\</strong> <strong> =\text{ }11/2\text{ }\left( 4\text{ }+\text{ }5 \right)/30 \\</strong> <strong> =\text{ }11/2\text{ }\left( 9/30 \right) \\</strong> <strong> =\text{ }11/2\left( 3/10 \right) \\</strong> <strong> =\text{ }33/20 \\</strong> <strong>\end{array}\]

i

More Material