Question

If the 4th term of a GP is the square of its second term and the first term is -2. Find the 7th term of the GP.

Answer 1

We have our first term of GP, a = -2

A GP is in form a, ar, ar², ar³....so on, where r = common ratio

So, 2nd term = -2r

4th term = -2r³

We are given

-2r³ = (-2r)²

-2r³ = 4r²

r = -2

So, we have both a and r with us,

So, a(n) term of GP is = ar ⁿ⁻¹

a(7th) = (-2)(-2)⁷⁻¹

= (-2)(-2)⁶

= (-2)⁷ = -128

Therefore, 7th term of GP is -128

Answer 2

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GiveN:

The 4th term of a G.P. is square of its 2nd term.

The first term is -3

To FinD:

The 7th term of the GP?

Step-wise-Step Explanation:

The general term of the GP is given by $\rm{a {r}^{n - 1} }$where a is the first term, r is the common ratio and n is the number of terms in that progression.

According to formula,

4th term = ar³

2nd term = ar

And,

⇒ 4th term = (2nd term)²

⇒ ar³ = (ar)²

⇒ ar³ = a²r²

⇒ ar³ / a²r² = 1

⇒ r / a = 1

⇒ a = r

It is given that a = -3, then r is also -3. We have to find the 7th term of the GP?

⇒ 7th term = ar⁶

⇒ 7th term = (-3)(-3)⁶

⇒ 7th term = (-3)⁷

⇒ 7th term = -2187

The required value of 7th term of the GP is -2187