What is the value of (91+92+93+⋯+140)?
- A5775
- B11550
- C17325
- D23100
Solution & Step-by-step Explanation
The given series is an Arithmetic Progression (AP):
91,92,93,…,140
Here:
First term (a) = 91
Last term (l) = 140
Common difference (d) = 1
The number of terms (n) can be calculated using the formula:
n=
d
l−a
+1
n=
1
140−91
+1=49+1=50
The sum of an AP (S
n
) is given by the formula:
S
n
=
2
n
×(a+l)
S
50
=
2
50
×(91+140)
S
50
=25×231
S
50
=5775
Therefore, the value of the series is 5775.
91,92,93,…,140
Here:
First term (a) = 91
Last term (l) = 140
Common difference (d) = 1
The number of terms (n) can be calculated using the formula:
n=
d
l−a
+1
n=
1
140−91
+1=49+1=50
The sum of an AP (S
n
) is given by the formula:
S
n
=
2
n
×(a+l)
S
50
=
2
50
×(91+140)
S
50
=25×231
S
50
=5775
Therefore, the value of the series is 5775.