Statement A (Assertion) : The common difference of the A.P. 19, 1… - Vidyadip

MCQ

Statement A (Assertion) : The common difference of the A.P. 19, 18, 17, ... is 1.
Statement R (Reason) : Let $a_1, a_2, a_3, a_4, \ldots$ is an A.P. Then, common difference of this A.P. will be the difference between any two consecutive terms, i.e., common difference $(d)=$ $a_2-a_1$ or $a_3-a_2$ or $a_4-a_3$ and so on.

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

✓

Answer

Correct option: D.

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

(d) : Clearly, Reason is true.
Given, A.P. is $19,18,17$, ...
Here, $a_1=19, a_2=18, a_3=17$ and so on.
$\therefore \quad$ Common difference $(d)=a_2-a_1=18-19=-1$
$\therefore \quad$ Assertion is false.

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