45 is a term of arithmetic sequence with common difference 2. Check whether the sum of any 17 terms of this sequence will be 2018? why?
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Answered by
2
Answer:
Jk
Step-by-step explanation:
Answered by
2
Step-by-step explanation:
We know that
s
n
=
n
2
(
2
a
+
(
n
−
1
)
d
)
Thus
186
=
12
2
(
2
a
+
(
11
)
d
)
186
=
6
(
2
a
+
11
d
)
31
=
2
a
+
11
d
Now we know that
t
n
=
a
+
(
n
−
1
)
d
.
83
=
a
+
(
20
−
1
)
d
83
=
a
+
19
d
We now have a system of equations:
{
31
=
2
a
+
11
d
83
=
a
+
19
d
Substituting (2) into (1), we get
31
=
2
(
83
−
19
d
)
+
11
d
31
=
166
−
38
d
+
11
d
−
135
=
−
27
d
d
=
5
Now solving for
a
:
83
−
19
(
5
)
=
−
12
The sum is once again given by
s
40
=
40
2
(
2
(
−
12
)
+
(
39
)
5
)
s
40
=
20
(
171
)
s
40
=
3420
Hopefully this helps!
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