Statement A (Assertion) : The numbers 4,1,-2,-5, are in A.P. Stat… - Vidyadip

MCQ

Statement A (Assertion) : The numbers $4,1,-2,-5, \ldots$ are in A.P.
Statement R (Reason) : An A.P. is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first two terms.

A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
✓
Assertion (A) is true but reason $(R)$ is false.
D
Assertion $(A)$ is false but reason $(R)$ is true.

✓

Answer

Correct option: C.

Assertion (A) is true but reason $(R)$ is false.

(c) : Clearly, statement-II is false.
Now, given numbers are $4,1,-2,-5, \ldots$
Here, $a_1=4, a_2=1, a_3=-2, a_4=-5, \ldots$
$
\begin{aligned}
\therefore \quad & a_2-a_1=1-4=-3, a_3-a_2=-2-1=-3, \\
& a_4-a_3=-5-(-2)=-3, \ldots
\end{aligned}
$
Now, $a_2-a_1=a_3-a_2=a_4-a_3=\ldots . .=-3$
$\therefore$ Givennumbers are in A.P.since ithas samecommon difference.

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