Question

Observe the given figure.

Which of the following is the correct representation of the triangular sum of the FOURTH square in the sequence?

• A. $25=12+13$
• B. $36=10+16$
• C. $25=10+15$
• D. $36=15+21$

Answer 1

The correct option is C

$25=10+15$

Observing the pattern we can have

$(2{)}^2=4=1+3=1+(1+2)$

$(3{)}^2=9=3+6=(1+2)+(1+2+3)$

$(4{)}^2=16=6+10=(1+2+3)+(1+2+3+4)$

Similarly proceeding further, we can have

$5^2=25=(1+2+3+4)+(1+2+3+4+5)=10+15$

Hence, representation of FOURTH term in sequence will be

$25=10+15$