find the 6th term of requence minus6,minus3,minus3/2??
Answers
Answer:
The sixth term of the given sequence is 1
Step-by-step explanation:
Given sequence is \frac{1}{6},\frac{1}{3},\frac{1}{2},...
6
1
,
3
1
,
2
1
,... are in AP
To find the sixth term of the given sequence :
Let a_1=\frac{1}{6}a
1
=
6
1
, a_2=\frac{1}{3}a
2
=
3
1
,a_3=\frac{1}{2}a
3
=
2
1
,...
Since the given sequence is in AP
Therefore the common difference d=a_2-a_1d=a
2
−a
1
Substitute the values in the formula we get
d=\frac{1}{3}-\frac{1}{6}d=
3
1
−
6
1
=\frac{2-1}{6}=
6
2−1
=\frac{1}{6}=
6
1
The common difference d=a_3-a_2d=a
3
−a
2
Substitute the values in the formula we get
d=\frac{1}{2}-\frac{1}{3}d=
2
1
−
3
1
=\frac{3-2}{6}=
6
3−2
=\frac{1}{6}=
6
1
Therefore the common difference is d=\frac{1}{6}d=
6
1
The general form of AP is a_n=a_1+(n-1)da
n
=a
1
+(n−1)d
Substitute n=6,a_1=\frac{1}{6}a
1
=
6
1
and d=\frac{1}{6}d=
6
1
in the above formula
a_6=\frac{1}{6}+(6-1)(\frac{1}{6})a
6
=
6
1
+(6−1)(
6
1
)
=\frac{1}{6}+(5)(\frac{1}{6})=
6
1
+(5)(
6
1
)
=\frac{1}{6}+\frac{5}{6}=
6
1
+
6
5
=\frac{1+5}{6}=
6
1+5
=\frac{6}{6}=
6
6
=1=1
Therefore a_6=1a
6
=1
Therefore the sixth term of the given sequence is 1