(Q26 ).Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.

(i) 2, 4, 8, 16, …….

(iii) – 1.2, – 3.2, – 5.2, – 7.2,……

(v) 3, 3 + √2, 3 + 2√2, 3 + 3√2, …….

(vii) 0, -4, -8, -12, …….

(ix) 1, 3, 9, 27,…..

(xi) a, a2, a3, a4, …..

(xiii) √3, √6, √9, √12, …….

(ii) 2,
5
2
 , 3,
7
2
 , ......

(iv) -10,-6, -2, 2, …….

(vi) 0.2, 0.22, 0.222, 0.2222, ……

(viii)
-1
2
 ,
-1
2
 ,
-1
2
 ,
-1
2

(x) a, 2a, 3a, 4a,….

(xii) √2, √8, √18, √32, …….

d
Given a2 - a1 a3 - a2 a4 - a3 If A.P or not Next three terms
(i) 2, 4, 8, 16, .... 'd' is not equal and not an A.P
(ii) 2,
5
2
 , 3,
7
2
 , .......
'd' is equal and forms an A.P
7
2
 +
= , 4 +
=
and
+
=
i.e., ,
,
(iii) -1.2, -3.2, -5.2, -7.2,..... - - - 'd' is equal and forms an A.P -, -, -
(iv) -10, -6, -2, 2, .... 'd' is equal and forms an A.P , ,
(v) 3, 3+√2, 3+2√2, 3+3√2,....... √ √ √ 'd' is equal forms an A.P 3+√2, 3+√2, 3+√2
(vi) 0.2, 0.22, 0.222, 0.2222, .... 'd' is not equal and does not form an A.P .........
(vii) 0, -4, -8, -12,....... - - - 'd' is equal and forms an A.P -, -, -
(viii) -
1
2
 , -
1
2
 , -
1
2
 , -
1
2
 , ....... 		'd' is equal and forms an A.P
-
, -
, -
(ix) 1, 3, 9, 27,.... 'd' is unequal and does not form an A.P .........
(x) a, 2a, 3a, 4a,....... 'd' is equal and forms an A.P , ,
(xi) a, a2, a3, a4.... 2 - 3 - 2 4 - 3 'd' is unequal and does not form an A.P .........

(xii) √2, √8, √18, √32,.......

i.e., √2, 2√2, 3√2, 4√2,.......

= √

= √

= √

 'd' is equal and forms an A.P

√, √, √

i.e., √2, √2, √2

(xiii) √3, √6,

√9, √12, .......

√ - √

√ - √

= - √

√ - √

= √ -

'd' is unequal and does not forms an A.P ................