the 4th term of a G.P. is square of its second term, and the first term is -3 determine its 7th term.
Answers
Answered by
128
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
Answered by
276
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 =
⇒ r = - 3
➠ Again,
↦ a₇ = ar⁶
↦ a₇ = (- 3) (- 3)⁶
↦ a₇ = (- 3)⁷
The 7th term of G.P. is
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