MCQ 11 Mark
Assertion $(A):$ Sum of first $10$ terms of the arithmetic progression $-0.5,-1.0,-1.5, \ldots$ is $27.5$
Reason $(R):$ Sum of n terms of an $A.P.$ is given as $S _{ n }=\frac{n}{2}[2 a+(n-1) d]$ where $a =$ first term, $d =$ common difference.
Reason $(R):$ Sum of n terms of an $A.P.$ is given as $S _{ n }=\frac{n}{2}[2 a+(n-1) d]$ where $a =$ first term, $d =$ common difference.
- ✓Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer
View full question & answer→Correct option: A.
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
Both are correct. Reason is the correct reasoning for Assertion.
Assertion, $S _{10}=\frac{10}{2}[2(-0.5)+(10-1)(-0.5)]$
$=5[-1-4.5]$
$=5(-5.5)$
$=27.5$
Assertion, $S _{10}=\frac{10}{2}[2(-0.5)+(10-1)(-0.5)]$
$=5[-1-4.5]$
$=5(-5.5)$
$=27.5$
