Question
Show that the progressions given below is an AP. Find the first term, common difference and next term.
$\sqrt{20},\sqrt{45},\sqrt{80},\sqrt{125},\ ....$
$\sqrt{20},\sqrt{45},\sqrt{80},\sqrt{125},\ ....$
✓
Answer
A sequence in which each term differs from its preceding term by a constant is called an AP.
$\sqrt{45}-\sqrt{20}=3\sqrt{5}-2\sqrt{5}=\sqrt{5}$
$\sqrt{80}-\sqrt{45}=4\sqrt{5}-3\sqrt{5}=\sqrt{5}$
$\sqrt{125}-\sqrt{80}=5\sqrt{5}-4\sqrt{5}=\sqrt{5}$
clearly, the progression an AP.
The first term $=\sqrt{20}=2\sqrt{5}$
common difference $=\sqrt{5}$
The next term $\sqrt{125}+\sqrt{5}=5\sqrt{5}+\sqrt{5}=6\sqrt{5}=\sqrt{180}$
$\sqrt{45}-\sqrt{20}=3\sqrt{5}-2\sqrt{5}=\sqrt{5}$
$\sqrt{80}-\sqrt{45}=4\sqrt{5}-3\sqrt{5}=\sqrt{5}$
$\sqrt{125}-\sqrt{80}=5\sqrt{5}-4\sqrt{5}=\sqrt{5}$
clearly, the progression an AP.
The first term $=\sqrt{20}=2\sqrt{5}$
common difference $=\sqrt{5}$
The next term $\sqrt{125}+\sqrt{5}=5\sqrt{5}+\sqrt{5}=6\sqrt{5}=\sqrt{180}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Mr.Jagadishprasad invest a sum of Rs. 75,000 in shares of face value 100 at Rs. 125 market value, then how many shares were purchased?
In the figure, $\triangle\text{ABC}$ is circumscribing a circle. Find the length of BC.
→Prove that:
$\frac{\sin18^\circ}{\cos72^\circ}+\sqrt{3}\big(\tan10^\circ\tan30^\circ\tan40^\circ\tan50^\circ\tan80^\circ\big)=2$
→→$\frac{\sin18^\circ}{\cos72^\circ}+\sqrt{3}\big(\tan10^\circ\tan30^\circ\tan40^\circ\tan50^\circ\tan80^\circ\big)=2$
In an A.P. $a=2$ and $d=3$, then find $S_{12}$.
→3 and -10
Which of the following are quadratic equations?
$\text{x}+\frac{1}{\text{x}}=\text{x}^2,\text{x}\neq0$
→$\text{x}+\frac{1}{\text{x}}=\text{x}^2,\text{x}\neq0$
Solve the following quadratic equation by factorization.
7m2 = 21m
7m2 = 21m
If two dice are rolled simultaneously, find the probability of the following events.
The sum of the digits on the upper faces is at least 10.
The sum of the digits on the upper faces is at least 10.
A metal parallelopiped of measures $16 cm \times 11 cm \times 10 cm$ was melted to make coins. How many coins were made if the thickness and diameter of each coin was 2 mm and 2 cm respectively? $\left(\pi=\frac{22}{7}\right)$
→