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1. Find:
Arithmetic Progression | Class 10 | ICSE | Maths | RD Sharma
1. Find:

(i) {{10}^{th}} tent of the AP 1,4,7,10….

(ii) {{18}^{th}} term of the AP \sqrt{2},3\sqrt{2},5\sqrt{2,}……. 

An arithmetic progression or arithmetic sequence is a number’s sequence such that the difference between the consecutive term is constant.

(i) Given A.P. is 1,4,7,10 ……….

First term \left( a \right)=1

Common difference  \left( d \right)= Second term – First term

=4-1=3.

We know that, {{n}^{th}} term in an A.P =a+\left( n-1 \right)d

Then, {{10}^{th}} term in the A.P is 1+\left( 10-1 \right)3

=1+9\times 3

=1+27

=28

\therefore {{10}^{th}} term of A. P. is 28

(ii) Given A.P. is \sqrt{2},3\sqrt{2},5\sqrt{2}, …….    

First term \left( a \right)=\sqrt{2}

Common difference = Second term – First term

=3\sqrt{2}-\sqrt{2}

⇒ d=2\sqrt{2}

We know that, {{n}^{th}} term in an A. P. =a+\left( n-1 \right)d

Then, {{18}^{th}} term of A. P. =\sqrt{2}+\left( 18-1 \right)2\sqrt{2}

=\sqrt{2}+17.2\sqrt{2}

=\sqrt{2}\left( 1+34 \right)

= 35\sqrt{2}

\therefore {{18}^{th}} term of A. P. is 35\sqrt{2}

i

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