Question

Which term of the Geometric progression 4, 4√2, 8……is 64√2

Answer 1

THE ANSWER TO THIS PROBLEM IS 10

Answer 2

Answer:

∴ 64√2, is the 10th term of the given geometric progression 4, 4√2, 8……

Step-by-step explanation:

Given,

Geometric Progression 4, 4√2, 8……

To find,

Which term of the given GP is  64√2

Solution:

Recall the formula

The nth term of a Geometric Progression = tₙ = arⁿ⁻¹ ----------------(1)

where 'a' is the first term and 'r' is the common ratio of the GP

Here the given GP is4, 4√2, 8……

The first term  = a = 4

The common ratio = r = $\frac{t_2}{t_1}$ = $\frac{4\sqrt{2} }{4}$ = $\sqrt{2}$

Let us take tₙ = 64√2

Then from equation (1), we have

arⁿ⁻¹ = 64√2

By substituting the values of 'a' and 'r' we get

4×(√2)ⁿ⁻¹  = 64√2

(√2)ⁿ⁻¹  = 16√2

(√2)ⁿ⁻¹  = 2⁴×√2

= (√2)²ˣ⁴ ×√2

=  (√2) ⁸⁺¹

=  (√2)⁹

(√2)ⁿ⁻¹  =  (√2)⁹

Comparing the exponents we get

n-1 = 9

n = 10

That is tₙ = 64√2, when n = 10

∴ 64√2, is the 10th term of the given geometric progression 4, 4√2, 8……

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