Answer :
Answer:
Option (C).
The twentieth term of the given arithmetic sequence is -36.
Step-by-step explanation:
The given arithmetic sequence is,
21, 18, 15, 12, ...........
Now, the first term of the arithmetic sequence, a₁ = 21
Second term of the arithmetic sequence, a₂ = 18
Third term of the arithmetic sequence, a₃ = 15
Fourth term of the arithmetic sequence, a₄ = 12
and so on.
Now, common difference, d = a₂ - a₁ = 18 - 21 = -3
We know that, [tex]n^{th}[/tex] term of an arithmetic sequence is given by,
aₙ = a₁ + (n - 1)d
To find the [tex]20^{th}[/tex] term of the given arithmetic sequence, we will substitute the values of a₁ , n and d in the above expression of aₙ.
Put a₁ = 21; n = 20 and d = -3 in the above expression of aₙ, we get
[tex]a_{20}=21+(20-1)(-3)=21+19\times(-3)=21-57=-36[/tex]
So, twentieth term of the given arithmetic sequence is -36.
Hence, option (C) is the correct answer.