Find the sum of all even integers between 101 and 999
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11th
Maths
Sequences and Series
Arithmetic Progression
Find the sum of all even in...
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Find the sum of all even integers between 101 and 999.
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ANSWER
The series is given as,
102,104,..........,998
a=102
d=104−102=2
a
n
=a+(n−1)d
998=102+(n−1)2
896=2(n−1)
448=n−1
n=449
S
n
=
2
n
[2a+(n−1)d]
S
449
=
2
449
[2(102)+(449−1)2]
=
2
449
×1100
=246,950
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