FIND GEOMETRIC SEQUENCE FROM THE GIVEN TWO TERMS

Find Geometric Sequence from the Given Two Terms :

In this section, we will learn how to find the geometric sequence from the given two terms.

Example 1 :

If the 4th and 7th terms of a G.P are 54 and 1458 respectively, find the G.P

Solution :

4th term  =  54

7th term  =  1458

t4 = 54

a r3  =  54   ----- (1)

t7  =  1458

a r6  =  1458  ----- (2)

(2)/(1)  =  (a r6)/(a r3)  ==>  1458/54

r3  =  27

r  =  3

By substituting r  =  3 in the first equation we get 

a (3) =  54

a(27)  =  54 

a  =  54/27

 a  =  2  

The general form of G.P is   a, a r , a r ²,.........

  =  2, 2(3), 2(3)2,..............

  =  2,6,18,............

Therefore the required geometric sequence is

2, 6, 18, .......

Example 2 :

In a geometric sequence, the first term is 1/3 and the sixth term is 1/729, find the G.P

Solution :

1st term  =  1/3

6th term = 1/729

a  =  1/3

t =  1/729

a r5  =  1/729  ------(1)

Applying the value of a in (1) we get, 

(1/3) r5  =  1/729

r5  =  (1/729) / (1/3)

r5  =  (1/729) ⋅ (3/1)

r5  =  1/243

r5  =  (1/3)5

r  =  1/3

The general form of G.P is   a, ar, ar2,.........

  =  1/3, (1/3) (1/3), (1/3)(1/3)²,..............

  =  1/3, 1/9, 1/27,............

Example 3 :

The fifth term of a G.P is 1875.If the first term is 3,find the common ratio.

Solution :

Fifth term (t5)  =  1875

ar4  =  1875 ----(1)

First term (a)  =  3

By applying the value of a in (1), we get 

3r4  =  1875

r4  =  1875/3

r4  =  625

r4  =  54

r  =  5

Therefore the common ratio is 5.

After having gone through the stuff given above, we hope that the students would have understood how to find the geometric sequence from the given two terms.

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