The 4^th term of a G.P is square of its second term, and the first term is - 3. Determine its 7^th term

Solution:

Let a be the first term and r be the common ratio of the G.P.

It is known that a = ar^{n - 1}

Therefore,

a₂ = ar¹ = (- 3) r

a₄ = ar³ = (- 3) r³

According to the question,

⇒ (- 3) r³ = [(- 3) r]²

⇒ - 3r³ = 9r²

⇒ r = - 3

Hence,

a = ar^{7 - 1}

= ar⁶

= ( -3)(- 3)⁶

= (- 3)⁷

= - 2187

Thus, the seventh term of the G.P is - 2187

---

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 4

The 4^th term of a G.P is square of its second term, and the first term is - 3. Determine its 7^th term

Summary:

We know that the 4th term of the G.P was the square of its second term and the first term is -3. The 7th term came out to be -2187