If S=125+224+323+......+242+251, then the value of S/900 is equal to

Correct answer: 3.25. S=∑r=125r26-r=26∑r=125r-∑r=125r^2 =26×(25×26)/2-(25×26×51)/6 =(25×26)/226-51/3=(25×2613)/2×9 ⇒S/900=13/4=3.25

Q7 / 118 · NTA Abhyas (JEE Main) 2020 · Mathematics · Sequences and Series

If $S = 1 (25) + 2 (24) + 3 (23) + . . . . . . + 24 (2) + 25 (1)$ , then the value of $\frac{S}{900}$ is equal to

Correct answer: 3.25

S = \sum_{r = 1}^{25} r (26 - r) = 26 \sum_{r = 1}^{25} r - \sum_{r = 1}^{25} r^{2}

= 26 \times \frac{25 \times 26}{2} - \frac{25 \times 26 \times 51}{6}

= \frac{25 \times 26}{2} (26 - \frac{51}{3}) = \frac{25 \times 2613}{2} \times 9

\Rightarrow \frac{S}{900} = \frac{13}{4} = 3.2 5

Hence, the correct answer is 3.25.