Show that each of the following sequences is an A.P. Also, find the common difference and write 3 more terms in each case.
i. `sqrt(2),\ 3sqrt(2),\ 5sqrt(2),\ 7sqrt(2) .......` ii. `9,7,5,3....`

Show that each of the following sequences is an A.P. Also, find the common difference and write 3 more terms in each case. i. 3,\ -1,\ -5,\ -9...... ii. -1,1//4,3//2, 11//4.....

Find: 18th term of the A.P. sqrt(2),\ 3sqrt(2),\ 5sqrt(2) ddot

Find: 18th term of the A.P. sqrt(2),\ 3sqrt(2),\ 5sqrt(2) ddot

Which of the following are A.P.'s ? If they form an A.P., find the common difference 'd' and write three more terms : (i) -10, -6, -2, 2, ..... " " (ii) 3, 3+sqrt(2), 3+2sqrt(2), 3+3sqrt(2), ... (iii) 0, -4, -8, -12, .... " " (iv) a, 2a, 3a, 4a, ..... (v) sqrt(3), sqrt(6), sqrt(9), sqrt(12), .....

Find sqrt(2+3sqrt(-5)) + sqrt(2-3sqrt(-5))

State in each case whether true or false: sqrt(2) + sqrt(3)= sqrt(5)

(sqrt(7)+2sqrt(3))(sqrt(7)-2sqrt(3))

State in each case whether true or false: 3sqrt(7)-2sqrt(7)= sqrt(7)

Which of the following are AP's ? If they form an AP, 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+sqrt2,3+2sqrt2,3+3sqrt2,..." " (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) sqrt2,sqrt8,sqrt18,sqrt32,..." " (xiii) sqrt3,sqrt6,sqrt9,sqrt12,..." " (xiv) 1^(2),3^(2),5^(2),7^(2),..." " (xv) 1^(2),5^(2),7^(2),73,...

Find the values of a and b in each of the (5+3sqrt(2))/(5-3sqrt(2))= a+b sqrt(2)