Do $4, 10, 16, 22, \ldots$ form an $AP$? If they form an $AP,$ write the next two terms.
(A) We have $a_{2}-a_{1} = 10-4 = 6$.
$a_{3}-a_{2} = 16-10 = 6$.
$a_{4}-a_{3} = 22-16 = 6$.
Since the difference $a_{k+1}-a_{k}$ is constant for all $k$,the given list of numbers forms an $AP$ with the common difference $d = 6$.
The next two terms are:
$22 + 6 = 28$
$28 + 6 = 34$.
$a_{3}-a_{2} = 16-10 = 6$.
$a_{4}-a_{3} = 22-16 = 6$.
Since the difference $a_{k+1}-a_{k}$ is constant for all $k$,the given list of numbers forms an $AP$ with the common difference $d = 6$.
The next two terms are:
$22 + 6 = 28$
$28 + 6 = 34$.
Explore More
Similar Questions
The sum of the third and the seventh terms of an $AP$ is $6$ and their product is $8$. Find the sum of the first sixteen terms of the $AP$.
Difficult
View SolutionFor the following $APs,$ write the first term and the common difference: $0.6, 1.7, 2.8, 3.9, \ldots$
Medium
View SolutionDo $1, 1, 1, 2, 2, 2, 3, 3, 3, \ldots$ form an $AP$? If they form an $AP$,write the next two terms.
Easy
View SolutionIn an $AP$,given $a_{3} = 15$ and $S_{10} = 125$,find $d$ and $a_{10}$.
Medium
View SolutionWrite the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -1.25, d = -0.25.$
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo