Question

Number of terms in the sequence $1,3,6,10,15,.5050$ is ?

• A. $101$
• B. $75$
• C. $100$
• D. $125$

Answer 1

The correct option is A $101$

Solution:

Let$y=1+3+6+10+15+21+.........5050$

$y=1+3+6+10+15+........T(n-1)+T\left(n\right)$

now by substract both eqn

$0=1+2+3+4+5+6+.....upto(n-1)term-T\left(n\right)$

$T\left(n\right)=\frac{n(n-1)}{2}$

$5050=\frac{n(n-1)}{2}$

$10100=n(n-1)$

by heat and trial method

$10100=101(101-1)$

thus number of term$\left(n\right)=101$