which of the following is not an arithmetic progression a) 1,3,9,27 b) -5,-3,-1,1 c) 2,6,10,14 d) 1,4,7,10
Answers
Answer:
I will try to solve it
.
.
..
hope it's helpful
Answer:
n = 26
Step-by-step explanation:
P dilip_k
Aug 1, 2018
I present here a trial solution.
Given
1
s
t
AP seies
1
,
8
,
15
,
22
...
.
And
2
n
d
AP series
2
,
13
,
24
,
35
...
...
Let
n
1
t
h
term of the first seies be a common intger with the
n
2
t
h
term of 2nd series.
So
1
+
(
n
1
−
1
)
⋅
7
=
2
+
(
n
2
−
1
)
⋅
11
⇒
7
n
1
+
3
=
11
n
2
By trial we get
For
n
1
=
9
,
20
,
31
,
42
...
.
the corresponding values of
n
2
=
6
,
13
,
20
,
27
...
.
.
we have
t
n
1
=
1
+
(
n
1
−
1
)
⋅
7
So inserting values of
n
1
we get the following series of common terms for two series.
1
+
(
9
−
1
)
⋅
7
=
57
1
+
(
20
−
1
)
.7
=
134
1
+
(
31
−
1
)
⋅
7
=
211
....etc
obviously we get the same series by inserting the values of
n
2
in
t
n
2
=
2
+
(
n
2
−
1
)
⋅
11
Hence common terms of both the series constitute an AP.
having first term
57
and common difference
77
Let the last common integer of the series be the
n
t
h
term of the series. This
n
t
h
must be
≤
2003
,the smaller last term of two given series.
Hence
57
+
(
n
−
1
)
⋅
77
≤
2003
⇒
n
≤
2023
77
⇒
n
≤
26
21
77
As
n
must be an integer.
n
=
26
Hence the number of common integers of two given serier is
n
=
26