Question

28.
Number of terms in the sequences 1, 3, 6, 10, 15, ..., 5050 is
1) 50
2) 75
3) 100
4) 125​

Answer 1

Answer:

3) 100

Step-by-step explanation:

If you observe the series given, you will understand that it is the series of sum of first n natural numbers.

1=1

3=1+2

6=1+2+3

10=1+2+3+4

.

.

.

So on

So we know that sum of first n natural numbers is:

Sn =

$\frac{n(n + 1)}{2}$

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If you put 100 in the above equation , you will get 5050 as your answer and you can observe,

Sn is the nth term.

hence 100 is your answer.

otherwise, you know that

$sn = \frac{n(n + 1)}{2} = nth \: term$

hence,

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

solving this you will get a quadratic equation with one variable "n".

solving this you will get n=100 and n= -101.

hence you will get n=100.

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