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Byju's Answer
Standard X
Mathematics
nth Term of an AP
The 4th term ...
Question
The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.
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Solution
We know that
T
n
=
a
+
(
n
−
1
)
d
Given,
T
4
=
a
+
(
4
−
1
)
d
=
0
a
+
3
d
=
0
a
=
−
3
d
T
25
=
a
+
(
25
−
1
)
d
=
a
+
24
d
=
(
−
3
d
)
+
24
d
=
21
d
And,
T
11
=
a
+
(
11
−
1
)
d
=
a
+
10
d
Then,
3
T
11
=
3
(
a
+
10
d
)
=
3
a
+
30
d
=
3
(
−
3
d
)
+
30
d
(
a
=
−
3
d
)
=
30
d
−
9
d
=
21
d
=
T
25
∴
3
T
11
=
T
25
Hence Proved.
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