Problems in progression
5. Find x in the series 1, 1/3, 0.2, x.
6. Find the 10th term of the progression 6/5, 4/3, 3/2 . . .
7. Find the sum of the first 10 terms of the Geometric Progression 2, 4, 8, 16 . . .
8. The fourth term of a geometric progression is 189 and the sixth term is 1701. Find the 8th term.
9. Find the sum of the infinite geometric progression 6, -2, 2/3 . . .
10. Find the fourth term of ½, 0.2, 0.125 . . .
z
Check the difference
d = 1/3 - 1 = -2/3
d = 0.2 - 1/3 = -2/15
Difference are not equal. Not an AP.
Check the ratio
r = 1/3 ÷ 1 = 1/3
r = 0.2 ÷ 1/3 = 3/5
Ratio are not equal. Not a GP.
Reciprocals: 1 ÷ 1, 1 ÷ 1/3, 1 ÷ 0.2 = 1, 3, 5
Check the difference
d = 3 - 1 = 2
d = 5 - 3 = 2
Difference are equal. The series is HP.
4th term = 5 + d = 7
Therefore, x = 1/7