Question

the 4th term of an gp is square of its second term and the first term is -3.determine its 7th term

Answer 1

Let 4 terms be a ar ar2 ar3
Acc. To ques.
A r cube = a2 r2
a =r

So common ratio is - 3

Seventh terms will be a multiply by r to the power 6

Here a is - 3
R is - 3

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