Discussion
The sides of 14 Square's are 11 cm, 12 cm, 13 cm, .......... 24 cm, then find the total area of 14 squares.
Answer: B
The total area is 4515 cm\(^{2}\).
The total is \(11^{2} + 12^{2} + \cdots + 24^{2}\). Use \(\sum_{k=1}^{n} k^{2} = \frac{n(n+1)(2n+1)}{6}\):
\[ \begin{aligned} \sum_{1}^{24} k^{2} &= \frac{24 \cdot 25 \cdot 49}{6} = 4900 \\ \sum_{1}^{10} k^{2} &= \frac{10 \cdot 11 \cdot 21}{6} = 385 \\ \text{total} &= 4900 - 385 = 4515 \end{aligned} \]
Subtracting the squares up to 11 instead of up to 10 would leave out the 11 cm square and give 4394, which is not offered; the other options do not come from the formula.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development