Progressions — Important Questions

2, 5, 8, 11, ..., 10, 7, 4, 1, ..., 5, 5, 5, 5, ...

A.P. has constant common difference. Option 1: d=3, Option 3: d=-3, Option 5: d=0. Option 2 is squares (not A.P.), Option 4 is G.P. (constant ratio).

1, 3, 9, 27, ..., 2, 4, 8, 16, ..., 1, -2, 4, -8, ...

G.P. has constant ratio. Option 1: r=3, Option 2: r=2, Option 4: r=-2. Options 3 and 5 are A.P. with constant differences.

-28

Using an = a + (n-1)d, we get a12 = 5 + (12-1)×(-3) = 5 + 11×(-3) = 5 - 33 = -28.

13

a = 7, d = 3, last term = 43. Using 43 = 7 + (n-1)×3, we get 36 = (n-1)×3, so n-1 = 12, therefore n = 13.