Question

54.(51+52+53+........+100) is equal to
ay 3775
b) 3757
c) 5737
d) 3755
how to solve this problem​

Answer 1

Answer:

we will add all of the integers likd 51+52+53-100whatcis the answer we will put that

Answer 2

Answer: (a) 3,775

Concept: This question can be solved by the 'Arithmetic Progression' concept. In Arithmetic progression, the Common difference between two consecutive numbers always remains the same.

Given: (51+52+53+..........+100)

To find: the sum of the above series

Solution:

Here first term a=51

Common difference d=1, $T_{n} = 100$

First, we find the number of terms by using a formula to find the general term

$T_{n}=a+(n-1)d$

$100=51+(n-1)1$

$n-1=49$

$n=50$

Now we will use the formula to find the sum of series

$S_{n}=\frac{n}{2}(a+a_{n})$

    $= \frac{50}{2}(51+100)$

    $=25(151)$

    $= 3,775$

Hence the option (a) 3,775 is sum of the series