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Question
Mathematics
Let the fourth term of an arithmetic progression be 6 and the m text th term be 18 . If A.P. has integral terms only, then the number of such A.P.s is
Q. Let the fourth term of an arithmetic progression be
6
and the
m
th
term be
18.
If
A
.
P
. has integral terms only, then the number of such
A
.
P
.s is ___
2308
208
Sequences and Series
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Answer:
9
Solution:
Given that
T
4
=
a
+
3
d
=
6
and
T
m
=
a
+
(
m
−
1
)
d
=
18
⇒
(
m
−
4
)
d
=
12
Since terms are integers, we have
(
m
−
4
)
=
±
1
,
±
2
,
±
3
,
±
4
,
±
6
,
±
12
But
m
>
0
∴
(
m
−
4
)
=
±
1
,
±
2
,
±
3
,
−
4
,
6
,
12
So,
m
has nine possible values.