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,
term of an arithmetic sequence is given by,
aₙ = a₁ + (n - 1)d
To find the
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
![a_{20}=21+(20-1)(-3)=21+19\times(-3)=21-57=-36](https://tex.z-dn.net/?f=a_%7B20%7D%3D21%2B%2820-1%29%28-3%29%3D21%2B19%5Ctimes%28-3%29%3D21-57%3D-36)
So, twentieth term of the given arithmetic sequence is -36.
Hence, option (C) is the correct answer.