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Home » Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms: (iii)     (iv)    
Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms: (iii)

    \[~\mathbf{2},\text{ }\mathbf{4},\text{ }\mathbf{8},\text{ }\mathbf{16},\text{ }\ldots \]

(iv)

    \[\mathbf{2},\text{ }\mathbf{5}/\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{7}/\mathbf{2},\text{ }\ldots \]

Arithmetic and Geometric Progression | Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal
Which of the following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms: (iii)

    \[~\mathbf{2},\text{ }\mathbf{4},\text{ }\mathbf{8},\text{ }\mathbf{16},\text{ }\ldots \]

(iv)

    \[\mathbf{2},\text{ }\mathbf{5}/\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{7}/\mathbf{2},\text{ }\ldots \]

From the question it is given that,

First term a =

    \[2\]

Then, difference d =

    \[4\text{ }\text{ }2\text{ }=\text{ }2\]

    \[\begin{array}{*{35}{l}} 8\text{ }\text{ }4\text{ }=\text{ }4 \\ 16\text{ }\text{ }8\text{ }=\text{ }8 \\ \end{array}\]

    \[16\text{ }\text{ }8\text{ }=\text{ }8\]

Therefore, common difference d is not same in the given numbers.

Hence, the numbers are not form A.P.

Solution:-

From the question it is given that,

First term a =

    \[2\]

Then, difference d =

    \[5/2\text{ }\text{ }2\text{ }=\text{ }\left( 5\text{ }\text{ }4 \right)/2\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]

    \[\begin{array}{*{35}{l}} 3\text{ }\text{ }5/2\text{ }=\text{ }\left( 6\text{ }\text{ }5 \right)/2\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2} \\ 7/2\text{ }\text{ }3\text{ }=\text{ }\left( 7\text{ }\text{ }6 \right)/2\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2} \\ \end{array}\]

Therefore, common difference d =

    \[{\scriptscriptstyle 1\!/\!{ }_2}\]

Hence, the numbers are form A.P.

i

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