Question

Assertion :Statement-1 If $a_1,a_2,a_3,..........,a_{24}$ are In A. P. such that $a_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225$ then $a_1+a_2+a_3+......+a_{23}+a_{24}=900$ because Reason: Statement-2 In any A.P. sum of the terms equidistant from begining and end is constant and is equal to
the sum of the first and the last term,

• A. Statement-1 is true, Statement-2 Is true and Statement-2 is correct explanation for Statement-1
• B. Statement-1 is true, Statement-2 Is true and Statement-2 is NOT correct explanation for Statement-1
• C. Statement-1 is true, Statement-2 is false
• D. Statement-1 is false, Statement-2 Is true

Answer 1

The correct option is A Statement-1 is true, Statement-2 Is true and Statement-2 is correct explanation for Statement-1

Assume $a_1+a_{24}=a_5+a_{20}=a_{10}+a_{15}=x$$,$ then $3x=225$.
$\Rightarrow x=75$
Also, $a_1+a_2+a_3+...+a_{23}+a_{24}=(a_1+a_{24})+(a_2+a_{23})+...+(a_{12}+a_{13})$
$\Rightarrow a_1+a_2+a_3+...+a_{23}+a_{24}=12x$
$\Rightarrow a_1+a_2+a_3+...+a_{23}+a_{24}=12x$
$\Rightarrow a_1+a_2+a_3+...+a_{23}+a_{24}=12\cdot 75$ $...(\because x=75)$
$\Rightarrow a_1+a_2+a_3+...+a_{23}+a_{24}=900$
Thus, Statement-1 is true, Statement-2 Is true and Statement-2 is correct explanation for Statement-1.