The first term of gp is -3 and the square of the second term is equal to its fourth term. Find it’s 7th term
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Answer:
a = r = -3
therefore 7th term is -2187
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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 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
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