2
You visited us
2
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
nth Term of A.P
In a H.P. T...
Question
In a H.P.
T
4
=
1
11
and
T
14
=
3
23
, then find
T
7
Open in App
Solution
It is given that
T
4
=
1
11
and
T
14
=
3
23
,
therefore, the reciprocals are the terms in A.P that are:
T
4
=
11
and
T
14
=
23
3
We know that the formula for the
n
th term of an A.P is
T
n
=
a
+
(
n
−
1
)
d
, where
a
is the first term,
d
is the common difference.
Thus,
a
+
3
d
=
11........
(
1
)
a
+
13
d
=
23
3
.
.
.
.
.
.
.
.
.
(
2
)
Subtract equation 1 from equation 2 as follows:
(
a
−
a
)
+
(
13
d
−
3
d
)
=
23
3
−
11
⇒
10
d
=
23
−
33
3
⇒
10
d
=
−
10
3
⇒
30
d
=
−
10
⇒
d
=
−
10
30
=
−
1
3
Substitute the value of
d
in equation 1:
a
+
3
d
=
11
⇒
a
+
(
3
×
−
1
3
)
=
11
⇒
a
−
1
=
11
⇒
a
=
11
+
1
=
12
Now, the first term
a
=
12
and the common difference
d
=
−
1
3
, therefore,
T
7
=
12
+
(
7
−
1
)
(
−
1
3
)
=
12
+
(
6
×
−
1
3
)
=
12
−
2
=
10
Hence, the
7
th term of H.P is
T
7
=
1
10
.
Suggest Corrections
0
Similar questions
Q.
In a H.P.
T
4
=
1
11
and
T
14
=
3
23
then find
T
19
Q.
(a) In a H.P,
find T
19
(b) In a H.P,
find T
7
and T
12