Question

If the 4th and 7th term of Geometric Progression are 54 and 1458 respectively,
find the Geometric Progression.​

Answer 1

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Answer 2

Answer:

Geometric Progression = 2,6,18,54,......

Step-by-step explanation:

Given : Fourth term = 54 and Seventh term = 1458

To find : Geometric Progression

Solution :

Given 4th term = 54

Formula= $t_{n} = ar^{n-1}$

So here n is 4

           $t_{4} = ar^{3}$ = 54    ----------------(i)

Given 7th term = 1458

Formula = $t_{n} = ar^{n-1}$

so here n is 7

              $t_{7} = ar^{6}$ = 1456   -----------(ii)

 Now equation (ii) ÷ (i)

$\frac{ar^{6} }{ar^{3} } = \frac{1456}{54}  = 26.96$ ≅ 27

     Therefore $r^{3} = 27$

                             r = 3

Substituting r = 3 in (i)

$ar^{3}  = 54$

$a(3)^{3}  = 54$

a = $\frac{54}{27}$

Therefore a = 2

Hence first term of Geometric progression is 2

Geometric progression's general form is $a, ar,ar^{2} ,ar^{3} , ...$

Therefore GP = $2,2(3),2(3)^{2} ,2(3)^{3}, .....$

                       = 2,6,18,54, ........