Question

what is the value of (91+92+93+..........+140)

Answer 1

91+92+93+---------------+140=6330

Answer 2

Answer: The value of (91+92+93+..........+140) is 5775.

Step-by-step explanation:

Here, the given expression is,

91+92+93+..........+140

Since, 91, 92, 93,......140 is an A.P. having the common difference of 1,

The first term of the series, $a_1=91$

And, the common difference, d = 1,

Last term, $a_n=140$

$\implies a_1+(n-1)d = 140\implies 91 + (n-1)=140\implies n = 140 - 90=50$

Thus, the number of the term of the A.P. is, n = 50.

⇒ The sum of the A.P.,

$S_n=\frac{n}{2}[2a_1+(n-1)d]$

$\implies S_{50}=\frac{50}{2}[2\times 91+(50-1)]$

$=25\times (182+49)=5775$

Hence, the value of (91+92+93+..........+140) is 5775.