Question

The geometric sequence 20, 60, 180, 540,.........., 393 660 has how many terms?

Answer 1

Answer: 10

Step-by-step explanation:

n'th term of an GP is

ar^(n-1),

where a is first term

n is n'th term and

r is common ratio.

here

a = 20 ,

r = 3 ,

n = we have to find.

Here lets consider last term as our n'th term

393660 = ar^(n-1)

substitute the value of a and r

3^(n-1) = 393660/20

3^(n-1) = 19683

3^(n-1) = 3^9

n-1 = 9

n = 10.......

Hope my answer helps you....

Answer 2

Answer:

10 terms

Step-by-step explanation:

GP : 20, 60, 180, 540, .... , 393660

According to the given GP, we can infer that,

⇒ First Term ( a ) = 20

⇒ Common Ratio ( r ) = a₂ / a₁ = 60 / 20 = 3

⇒ Last term ( arⁿ⁻¹ ) = 393660

Therefore we are required to find 'n'

⇒ arⁿ⁻¹ = 393660

⇒ 20 ( 3 ) ⁿ⁻¹ = 393660

⇒ ( 3 ) ⁿ⁻¹ = 393660 / 20 = 19683

Now Prime factorisation of 19683 = 3⁹

⇒ ( 3 ) ⁿ⁻¹ = 3⁹

Since bases are same, we can equate the powers.

⇒ n - 1 = 9

⇒ n = 9 + 1 = 10

Hence there are 10 terms in the given GP.