which of the following is not Arthemetic progression
-1.2,0.8,2.8
3,3+under root 2,3+under root 2,3+3under root
4/3,7/3,9/3,12/3
-1/5,-2/5,-3/5
Answers
Step-by-step explanation:
For Arithmetic progression the series have common difference in two consecutive terms i.e. a_2-a_1=a_3-a_2a
2
−a
1
=a
3
−a
2
(A) - 1.2, 0.8, 2.8, ...
Here, a_1=-1.2,a_2=0.8,a_3=2.8a
1
=−1.2,a
2
=0.8,a
3
=2.8
0.8-(-1.2)=2.8-0.80.8−(−1.2)=2.8−0.8
2=22=2
So, the series given is an A.P.
(B) 3,3+\frac{1}{2},3+\frac{2}{2},3+\frac{3}{2},..3,3+
2
1
,3+
2
2
,3+
2
3
,..
Here, a_1=3,a_2=3+\frac{1}{2}=\frac{7}{2},a_3=3+\frac{2}{2}=4a
1
=3,a
2
=3+
2
1
=
2
7
,a
3
=3+
2
2
=4
\frac{7}{2}-3=4-\frac{7}{2}
2
7
−3=4−
2
7
\frac{1}{2}=\frac{1}{2}
2
1
=
2
1
So, the series given is an A.P.
(C) 4,7,9,12,..
Here, a_1=4,a_2=7,a_3=9a
1
=4,a
2
=7,a
3
=9
7-4=9-77−4=9−7
3\neq 23
=2
So, the series given is not an A.P.
Therefore, option C is correct.
#Learn more
Q. Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(i) 2, 4, 8, 16 …
(ii) 2, 5/2, 3, 7/2 ....
(iii) -1.2, -3.2, -5.2, -7.2 …
(iv) -10, - 6, - 2, 2 …
(v) 3, 3 + √2, 3 + 2√2, 3 + 3√2
(vi) 0.2, 0.22, 0.222, 0.2222 ….
(vii) 0, - 4, - 8, - 12 …
(viii) -1/2, -1/2, -1/2, -1/2 ....
(ix) 1, 3, 9, 27 …
(x) a, 2a, 3a, 4a …
(xi) a, a2, a3, a4 …
(xii) √2, √8, √18, √32 ...
(xiii) √3, √6, √9, √12 ...
(xiv) 12, 32, 52, 72 …
(xv) 12, 52, 72, 73 …