GATE ECE 2026 | GA | Question: 8

Question

Let $P_{k}$ represent the perimeter of a square with sides of length $k$. The value of the expression $P_{1}+P_{2}+P_{3}+\cdots+P_{10}$ is $\_\_\_\_$

• A. $55$
• B. $110$
• C. $220$
• D. $440$

Answer 1

Option C is correct 

Answer 2

Pk = perimeter of sqr. = 4 * k (where k= length of sides)

 

SERIES (S) = P1​+P2​+P3​+⋯+P10​ = 4*1+4*2+4*3+.....+4*10 = 4+8+12+.....+40

the series turned out to be an AP series with:

first term = a = 4

last term = l = 40

commom/constant difference = d = a2-a1 = 8-4 = 4

sum of n term in AP = Sn = n/2(a+l)= n/2 [2a+(n-1d)]

S10 = 10/2(4+40) = 5*44 = 220

 

thus 220 (option C)