Which of the following are Aps? If they form an AP, find the common difference d and write the next three 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+sqrt(2), 3+2sqrt(2), 3+3sqrt(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, a^(2), a^(3), a^(4)`,.........
(xii) `sqrt(2), sqrt(8), sqrt(18), sqrt(32)`,......
(xiii) `sqrt(3), sqrt(6), sqrt(9), sqrt(12)`,...............

Answer

(i) Not AP
(ii) AP, next three terms =4 `,9/2, 5`
(iii) AP, next three terms `=-9.2, -11.2, -13.2`
(iv) AP, next three terms =6,10,14
(v) AP, next three terms `=3+4sqrt(2), 3+5sqrt(2), 3+6sqrt(2)`
(vi) Not AP
(vii) AP, nesxt three terms `=-16, -20, -24`
(viii) AP, next three terms `=-1/2, -1/2, -1/2`
(ix) Not AP
(x) AP, next three term = 5a, 6a, 7a
(xi) Not AP
(xii) AP, next three terms `=sqrt(50), sqrt(72), sqrt(96)`
(xiii) Not AP