Find the common difference of an A.P. 5/4 2, 11/4 , 14/4
Answers
Answer:
z00 M, Id:6849304329, P:12345
Answer:
Given A.P is
−1,
4
1
,
2
3
,....
the common difference of an A.P is given by d=a
n+1
−a
n
by putting n=1 in above equation
d=a
2
−a
1
=(
4
1
)−(−1)
d=
4
1
+1
d=
4
5
first term of this A.P is
a
1
=−1
the nth term of this A.P is given by
a
n
=a
1
+(n−1)d
⟹a
n
=−1+(n−1)(
4
5
)
⟹a
n
=−1+
4
5
n−
4
5
⟹a
n
=−
4
9
+
4
5
n….eq(1)
finding next four terms of A.P
1) for finding the 4th term of sequence (a
4
) put n=4 in eq(1)
⟹a
4
=
4
−9
+
4
5
×4
⟹a
4
=
4
−9
+
4
20
⟹a
4
=
4
11
2) for finding the 5th term of sequence (a
5
) put n=5 in eq(1)
⟹a
5
=
4
−9
+
4
5
×5
⟹a
5
=
4
−9
+
4
25
⟹a
5
=
4
16
⟹a
5
=4
3) for finding the 6th term of sequence (a
6
) put n=6 in eq(1)
⟹a
6
=
4
−9
+
4
5
×6
⟹a
6
=
4
−9
+
4
30
⟹a
6
=
4
21
4) for finding the 7th term of sequence (a
7
) put n=7 in eq(1)
⟹a
7
=
4
−9
+
4
5
×7
⟹a
7
=
4
−9
+
4
35
⟹a
7
=
4
26
⟹a
7
=
2
13