Question

Which term of the G.P :6,-12,24,-48 is 384?

Answer 1

Answer:

7th term

Step-by-step explanation:

a (First term)= 6

r (Common Ratio) = -12/6 = -2

Tn = ar^n-1

384 = (6)×(-2)^n-1

384/6 = (-2)^n-1

64 = (-2)^n-1

(-2)⁶ = (-2)^n-1

6 = n - 1

6 + 1 = n

n = 7

7th term = 384

Answer 2

Therefore, 384 is the 7th term of the given GP

Given,

GP: 6, -12, 24, -48, ...

To Find,

n such that a(n) = 384

Solution,

From the given GP, we can see the following:

first term = a = 6

common ratio = r = a(2) ÷ a(1) = -12 ÷ 6 = -2

Now, nth term of a GP is given by ar^n

ar^(n-1) = 384

⇒ 6 x (-2)^(n-1) = 384

⇒ (-2)^(n-1) = 384 ÷ 6 = 64

⇒ n-1 = 6

⇒ n = 7

Therefore, 384 is the 7th term of the given GP

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