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
Does the sequence $-2, 2, -2, 2, -2, \ldots$ form an $AP$? If it forms an $AP$,write the next two terms.
Easy
View SolutionWhich term of the $AP : 3, 8, 13, 18, \ldots$ is $78$ (in $^{th}$)?
Medium
View SolutionIn an $AP$,given $l = 28$,$S = 144$,and there are a total of $9$ terms. Find $a$.
Easy
View SolutionIf the sum of the first $n$ terms of an $AP$ is $4n - n^2$,what is the first term (that is $S_1$)? What is the sum of first two terms? What is the second term? Similarly,find the $3^{rd}$,the $10^{th}$ and the $n^{th}$ terms.
Difficult
View SolutionChoose the correct choice in the following and justify: the $11^{th}$ term of the $AP: -3, -\frac{1}{2}, 2, \ldots$ is
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