The document defines geometric progressions as sequences where the ratio between successive terms is constant. It provides examples of geometric progressions and expresses the general form as a, ar, ar2, ar3, etc., where a is the first term and r is the common ratio. Formulas are given for the nth term and sum of n terms of a geometric progression. Several examples are then worked through applying these formulas to find specific terms and sums of terms for given progressions.

1. Geometic Progressions

2. Geometric Progression
 If in a sequence the ratio of any term to its
preceding term is constant, it is called
geometric progression.
 The constant ratio is called the comman
ratio.
 Eg. 5, 15, 45, 135, 405, … is a GP
 Whose common ratio is 3

3. Geometric Progression
 If a is the first term and r is the common
ratio o a GP, it can be expressed as:
 a, ar, ar2, ar3, ar4, … this general form of
GP

4. nth term of GP
 Let a, ar, ar2, ar3, ar4, … be a GP
 Here T1 = a = ar1-1
 T2 = ar = ar2-1
 T3 = ar2 = ar3-1
 T4 = ar3 = ar4-1
 Tn = a rn-1

5. Sum of n terms of GP
 Let a, ar, ar2, ar3, ar4, … be a GP
 Sn = a + ar + ar2 + ar3 + … + a rn-1
 Sn = a (1 – rn) / (1 – r) {if r < 1
 Sn = a (rn – 1) / (r – 1) {if r > 1

6. Ex.1
 Find the required term of the following
progressions:
 (i) 2, 6, 18, 54, … (9th term)
 (ii) 1024, -512, 256, -128, … (10th term)
 (iii) 5, 25, 125, 625, … (40th term)

7. Ex.2
 Find the sum up to the required term of
the following progressions:
 (i) 1, 2, 4, 8, 16, … (up to 12 terms)
 (ii) 2, 10, 50, 250 , … (up to 9 terms)
 (iii)8, 4, 2, 1, … (40th term)

8. Ex.3
 The fourth term of a GP is 4 and the
product of second and the fourth terms is
1.
 Find the sixth term and sum to first 6
terms.

9. Ex.4
 The fourth and the seventh terms of a GP
are 72 and 576.
 Find the sum of first n terms.

10. Ex.5
 Three numbers are in GP. Their sum and
product are 28 and 512 respectively. Find
the numbers.