Find the sum of all odd numbers from 1 to 150.
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Answered by
0
Answer:
Answer is 5625
Step-by-step explanation:
The odd natural numbers from 1 to 150 are:1,3,5,7,9 to 149, therefore, Sum of all odd numbers from 1 to 150 is 5625
Answered by
1
Answer:
5625
Step-by-step explanation:
Odd numbers from 1 to 150 are 1,3, 5, 7, …, 149 Here, difference between any two consecutive terms is 2.
∴ It is an A.P.
∴ a = 1, d = 2
(i) Let us find how many odd numbers are there from 1 to 150, i.e.
find the value of n if
tn = 149
tn = a + (n – 1)d
∴149 = 1 + (n – 1)2
∴ 149 – 1 = (n – 1)2
∴ 148/2 = n – 1
∴ 74 = n – 1
∴ n = 74 + 1 = 75
ii) now , find the sum
t1=a=1, tn=149, n=75
∴ Sn=n/2*(t1+tn)
∴S75=75/2*(1+149)
=75/2*(150)
=75*75
∴S75=5625
hence,the sum of all odd numbers from 1 to 150 is 5625.
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