Are $1, 3, 9, 27, \ldots$ in $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.
(NONE) Given sequence: $1, 3, 9, 27, \ldots$
To check if the sequence is an $AP$,we calculate the difference between consecutive terms:
$a_{2} - a_{1} = 3 - 1 = 2$
$a_{3} - a_{2} = 9 - 3 = 6$
$a_{4} - a_{3} = 27 - 9 = 18$
Since the common difference $(a_{k+1} - a_{k})$ is not constant (i.e.,$2 \neq 6 \neq 18$),the given sequence does not form an $AP$.
To check if the sequence is an $AP$,we calculate the difference between consecutive terms:
$a_{2} - a_{1} = 3 - 1 = 2$
$a_{3} - a_{2} = 9 - 3 = 6$
$a_{4} - a_{3} = 27 - 9 = 18$
Since the common difference $(a_{k+1} - a_{k})$ is not constant (i.e.,$2 \neq 6 \neq 18$),the given sequence does not form an $AP$.
Explore More
Similar Questions
In an $AP$,given $l = 28$,$S = 144$,and there are a total of $9$ terms. Find $a$.
Easy
View SolutionWrite the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a=4, d=-3.$
Medium
View SolutionIn which of the following situations,does the list of numbers involved make an arithmetic progression,and why? The amount of money in the account every year,when ₹ $10000$ is deposited at compound interest at $8 \%$ per annum.
Difficult
View SolutionIn an $AP$ given $a=5, d=3, a_{n}=50,$ find $n$ and $S_{n}$.
Easy
View Solution$a, 2a, 3a, 4a, \dots$ are $APs$? If they form an $AP,$ find the common difference $d$ and write three more terms.
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