The sum of all numbers from 1 to 1000, which are neither divisible by 2 nor by 5 is
Answers
Answered by
1
Answer:
The sum is
3050
.
Explanation:
Ths sum of arithmetric progression is
S
=
n
2
(
a
+
l
)
, where
n
is the number of terms,
a
is the first term and
l
is the last term.
The sum of integres
1
to
100
which is divisible by
2
is
S
2
=
2
+
4
+
6
+
…
100
=
50
2
⋅
(
2
+
100
)
=
2550
and, the sum of integers divisible by
5
is
S
5
=
5
+
10
+
15
+
…
100
=
20
2
⋅
(
5
+
100
)
=
1050
You may think the answer is
S
2
+
S
5
=
2550
+
1050
=
3600
but this is wrong.
2
+
4
+
6
+
…
100
and
5
+
10
+
15
+
…
100
have common terms.
They are integers divisible by
10
, and their sum is
S
10
=
10
+
20
+
30
+
…
100
=
10
2
⋅
(
10
+
100
)
=
550
Therefore, the answer for this question is
S
2
+
S
5
−
S
10
=
2550
+
1050
−
550
=
3050
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