Question

the 4th term of a G.P. is square of its second term, and the first term is -3 determine its 7th term.​

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

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

Answer 2

Answer:

✯ Given :-

• The 4th term of a G.P. is a square of its second term and the first term is -3

✯ To Find :-

• What is the 7th term of G.P.

✯ Solution :-

⋆ Given :-

• 4th term = (2nd term)²
• a = - 3

➣ According to the question,

⇒ a₄ = (a₂)²

⇒ ar³ = (ar)²

⇒ ar³ = a²r²

⇒ (- 3)r³ = (- 3)²r²

⇒ - 3r = 9

⇒ r = $\dfrac{9}{- 3}$

⇒ r = - 3

➠ Again,

↦ a₇ = ar⁶

↦ a₇ = (- 3) (- 3)⁶

↦ a₇ = (- 3)⁷

$\therefore$ The 7th term of G.P. is $\boxed{\bold{\large{( - 3)⁷}}}$

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