HOW TO FIND WHICH TERM OF THE GEOMETRIC SEQUENCE IS GIVEN

How to Find Which Term of the Geometric Sequence is Given ?

In this section, we will see some examples to understand how we find which term of the geometric is given.

Example 1 :

Which term of the geometric sequence

5, 2, 4/5, 8/25,...............is 128/15625 ?

Solution :

Let 128/15625 be the n^th term of the given geometric sequence .

t_n  =  128 / 15625

ar^(n-1)  =  128 / 15625

a  =  5, r = 2/5

5 (2/5)^(n-1)  =  128/15625

(2/5)^(n-1)  =  128 / (15625 ⋅ 5)

(2/5)^(n-1)  =  2⁷ / (5⁶ ⋅ 5)       

(2/5)^(n-1)  =  2⁷/5⁷

(2/5)^(n-1)  =  (2/5)⁷

Since the bases are equal, we can equate the powers

n - 1  =  7

n  =  8

Therefore the 8^th term of the given geometric sequence is 128/15625.

Example 2 :

Which term of the geometric sequence

1, 2, 4, 8,..........is 1024 ?

Solution :

Let 1024 be the n^th term of the given geometric sequence.

t_n  =  1024

ar^(n-1)  =  1024

a  =  1 and r  =  2

1 (2)^(n-1)  =  1024

2^(n-1)  =  2¹⁰

n - 1  =  10

n  =  11

Therefore the 11^th term of the given sequence is 1024.

After having gone through the stuff given above, we hope that the students would have understood how to find which term of the geometric sequence is given.

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