Question

Find the nth term of 5, 10, 20, 40, ………​

Answer 1

Answer:

your answer is this....

Step-by-step explanation:

1280

Answer 2

Answer :

nth term of 5 , 10 , 20 , 40 , .... = 5(2)ⁿ⁻¹

Step-by-step explanation :

$\underline{\bf Geometric \ Progression:}$

• It is the sequence of numbers such that the ratio between any two successive terms is constant.

• General form of G.P.,

        a , ar , ar² , ar³ ,....

________________________

Given series,

5 , 10 , 20 , 40 , ....

first term, a₁ = a = 5

second term, a₂ = 10

third term, a₃ = 20

fourth term, a₄ = 40

⇒ Common difference is the difference between two successive terms.

 d = a₄ - a₃ = a₃ - a₂ = a₂ - a₁

a₄ - a₃ = 40 - 20 = 20

a₃ - a₂ = 20 - 10 = 10

a₂ - a₁ = 10 - 5 = 5

Since, the difference between any two successive terms is not constant, the series are not in A.P.

⇒ Common ratio is the ratio between a term and the term preceding it.

  r = a₄/a₃ = a₃/a₂ = a₂/a₁

a₄/a₃ = 40/20 = 2

a₃/a₂ = 20/10 = 2

a₂/a₁ = 10/5 = 2

Since it is constant, the given series are in G.P.

Therefore, common ratio, r = 2

In G.P.,

nth term is given by,

aₙ = arⁿ⁻¹

Substituting the values,

→ aₙ = 5(2)ⁿ⁻¹

Verification :

2nd term = 10

5(2)²⁻¹ = 10

5(2)¹ = 10

5(2) = 10

10 = 10

3rd term = 20

5(2)³⁻¹ = 20

5(2)² = 20

5(4) = 20

20 = 20

Hence verified!