Question

A twenty storied building was observed from outside, each floor has a kite shaped figure which gets on magnifying as observed from the $1^{st}$ to ${20}^{th}$ floor. The area of first five kites on each floor was calculated and they were found to develop a pattern. These five areas are ${10m}^2$, ${15m}^2$ , ${20m}^2$, ${25m}^2$, ${30m}^2$ and so on. The area of the kite on the top floor is ____.

• A. ${100m}^2$
• B. ${105m}^2$
• C. ${110m}^2$
• D. ${200m}^2$

Answer 1

The correct option is

C

${105m}^2$

Given 10, 15, 20, 25, 30..........

,The sequence of the areas on each floor forms an Arithmetic Progression, with first term as 10 and common difference as 5.

General term $T_n=a+(n-1)d$
$=10+(n-1)5$

We require,$T_{20}=10+(20-1)5=10+19\times 5=105$