Write the first three terms of the APs when $ a $ and $ d $ are as given below:
$ a=\sqrt{2}, \quad d=\frac{1}{\sqrt{2}} $
Given:
\( a=\sqrt{2}, d=\frac{1}{\sqrt{2}} \)
To do:
We have to write the first three terms of the given arithmetic progression.
Solution:
First term $a_1=a=\sqrt{2}$
Second term $a_2=a_1+d=\sqrt{2}+\frac{1}{\sqrt{2}}=\frac{\sqrt2 \times \sqrt2+1}{\sqrt2}=\frac{2+1}{\sqrt{2}}=\frac{3}{\sqrt{2}}$
Third term $a_3=a_2+d=\sqrt{2}+\frac{2}{\sqrt{2}}=\frac{\sqrt2 \times \sqrt2+2}{\sqrt2}=\frac{2+2}{\sqrt{2}}=\frac{4}{\sqrt{2}}$
Therefore, the first three terms of the given AP are $\sqrt{2}, \frac{3}{\sqrt{2}}, \frac{4}{\sqrt{2}}$.
Related Articles
- Write the first three terms of the APs when \( a \) and \( d \) are as given below:\( a=\frac{1}{2}, d=-\frac{1}{6} \)
- Write the first three terms of the APs when \( a \) and \( d \) are as given below:\( a=-5, d=-3 \)
- Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows:$a = -1, d = \frac{1}{2}$
- Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows:$a = -2, d = 0$
- Write the arithmetic progression when first term a and common difference d are as follows:$a = -1, d= \frac{1}{2}$
- Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.$-\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, …….$
- Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows:(i) $a = 10, d = 10$(ii) $a = -2, d = 0$(iii) $a = 4, d = -3$(iv) $a = -1, d = \frac{1}{2}$(v) $a = -1.25, d = -0.25$
- Simplify the following:$(\frac{\sqrt{3}}{\sqrt{2}+1})^2 + (\frac{\sqrt{3}}{\sqrt{2}-1})^2 +(\frac{\sqrt{2}}{\sqrt{3}})^2 $
- Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.(i) \( 2,4,8,16, \ldots \)(ii) \( 2, \frac{5}{2}, 3, \frac{7}{2}, \ldots \)(iii) \( -1.2,-3.2,-5.2,-7.2, \ldots \)(iv) \( -10,-6,-2,2, \ldots \)(v) \( 3,3+\sqrt{2}, 3+2 \sqrt{2}, 3+3 \sqrt{2}, \ldots \)(vi) \( 0.2,0.22,0.222,0.2222, \ldots \)(vii) \( 0,-4,-8,-12, \ldots \)(viii) \( -\frac{1}{2},-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}, \ldots \)(ix) \( 1,3,9,27, \ldots \)(x) \( a, 2 a, 3 a, 4 a, \ldots \)(xi) \( a, a^{2}, a^{3}, a^{4}, \ldots \)(xii) \( \sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \ldots \)(xiii) \( \sqrt{3}, \sqrt{6}, \sqrt{9}, \sqrt{12}, \ldots \)(xiv) \( 1^{2}, 3^{2}, 5^{2}, 7^{2}, \ldots \)(xv) \( 1^{2}, 5^{2}, 7^{2}, 73, \ldots \)
- If \( \sin \mathrm{A}=\frac{1}{2} \), then the value of \( \cot \mathrm{A} \) is(A) \( \sqrt{3} \)(B) \( \frac{1}{\sqrt{3}} \)(C) \( \frac{\sqrt{3}}{2} \)(D) 1
- Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.$\sqrt2, \sqrt8, \sqrt{18}, \sqrt{32}, …..$
- Simplify:\( \frac{1}{2+\sqrt{3}}+\frac{2}{\sqrt{5}-\sqrt{3}}+\frac{1}{2-\sqrt{5}} \)
- Write the Polynomial whose zeroes are $\sqrt{\frac{3}{2}}, -\sqrt{\frac{3}{2}}$.
- Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows:$a = 4, d = -3$
- Write first four terms of the AP, when the first term $a$ and the common difference $d$ are given as follows:$a = -1.25, d = -0.25$
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies