Finding the GENERAL TERM OR FORMULA for the nth term of an Arithmetic Sequence

Hi Guys!!! I'm your MathematiSEAN
This video is all about Finding the General term or Formula for the nth term of an Arithmetic Sequence.

For example, the terms of a Sequence are known, For example: 6, 11, 16, 21, 26, ... ,
and we want to write a formula that will produce those terms. What we're going to do is to use the Formula for the nth term of an Arithmetic Sequence: " aₙ = a₁ + ( n - 1 ) d " in order to find the General term of the given Sequence.

First thing to do is to find the value of first term and the value of the common difference which can be found right away in the given Sequence.

a₁ = 6
d = 5

Second is to plug in those values in the formula and solve it.
aₙ = a₁ + ( n - 1 ) d
= 6 + (n - 1 ) 5
= 6 + 5n - 5
= 1 + 5n

The General term for the Sequence 6, 11, 16, 21, 26, ... , is 1+ 5n

Now solve for the terms of the Sequence using the General term or the formula for that given Sequence

a₁= 1 + 5(1) = 6
a₂= 1 + 5(2) = 11
a₃= 1 + 5(3) = 16
a₄= 1 + 5(4) = 21
a₅= 1 + 5(5) = 26

The General term produced the same terms in
the given Sequence. Therefore our answer is Correct.

UNDERSTANDING THE CONCEPT OF THE FORMULA FOR FINDING THE NTH TERM OF AN ARITHMETIC SEQUENCE

[mrae_me]

Thank you for making this video 😊 it helps me to understand a lot