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# 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,

a_{2} = ar^{1} = (- 3) r

a_{4} = ar^{3} = (- 3) r^{3}

According to the question,

⇒ (- 3) r^{3} = [(- 3) r]^{2}

⇒ - 3r^{3} = 9r^{2}

⇒ r = - 3

Hence,

a = ar^{7 }^{- }^{1}

= ar^{6}

= ( -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

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