Is 2021 belongs to the arithmetic sequence with first term 4 and common difference 7?
(b)
Check wether 2021 is the difference of two terms of the above sequence.
Answers
Step-by-step explanation:
Given :-
First term = 4
Common difference = 7
To find:-
Is 2021 belongs to the arithmetic sequence with first term 4 and common difference 7?
Check wether 2021 is the difference of two terms of the above sequence.
Solution:-
Given that
First term of an AP (a) = 4
Common difference (d) = 7
Let the nth term of the AP (an) = 2021
We know that
The General term or nth term of an AP is
an = a+(n-1)d
=> an = 2021
=> a+(n-1)d = 2021
=> 4+ (n - 1) (7) = 2021
=> 4 +7n -7 = 2021
=> 7n -3 = 2021
=> 7n = 2021+3
=> 7n = 2024
=> n = 2024/7
=> n = 289.14...
But n cannot be a fraction or a decimal number
It must be a natural number.
2021 is not in the given AP.
Given that a = 4 ,d = 7
The general form of an AP :
a,a+d,a+2d,....
a = 4
a+d = 4+7 = 11
a+2d = 4+2(7)=4+14 = 18
a+3d = 4+3(7)=4+21=25
The AP : 4,11,18,25,...
Answer:-
2021 is not the term of the given Arithmetic Progression.
Used formulae:-
The General term or nth term of an AP is
an = a+(n-1)d
a = First term
d = Common difference
n = number of terms