Respuesta :

LeeDanHaa

Answer:

Step-by-step explanation:

Number series : 9, 14, 19, 24

First term = a1 = 9

common difference = a2 - a1 = 14 - 9=5

Find the nth term:

an = a1 + + (n - 1)d

an = 9+ (n - 1)(5)

an = 9+5n - 5

an = 4 + 5n

Find the 10th term:

an = 4 + 5n

a10 = 4 + 5(10)

a10 = 4 + 50

a10 = 54

Find the 50th term:

an = 4 + 5n

a50 = 4 + 5(50)

a50 = 254

Find the difference between the 10th and

50th term:

Difference = 254 - 54 = 200

Answer: The difference is 200

Eduard22sly

Given the data from the question, the difference between the 10th term and the 50th term is 200

What is an arithmetic sequence?

This is a type of sequence which have common difference between each term. It is represent mathematically as:

Tₙ = a + (n – 1)d

Where

  • Tₙ is the nth term
  • a is the first term
  • n is the number of terms
  • d is the common difference

How to determine the 10th term

  • Sequence: 9,14,19, 24
  • First term (a) = 9
  • Common difference = 14 – 19 = 5
  • Number of terms (n) = 10
  • 10th term (T₁₀) =?

Tₙ = a + (n – 1)d

T₁₀ = 9 + (10 – 1)5

T₁₀ = 9 + (9)5

T₁₀ = 9 + 45

T₁₀ = 54

How to determine the 50th term

  • Sequence: 9,14,19, 24
  • First term (a) = 9
  • Common difference = 14 – 19 = 5
  • Number of terms (n) = 50
  • 50th term (T₅₀) =?

Tₙ = a + (n – 1)d

T₅₀ = 9 + (50 – 1)5

T₅₀ = 9 + (49)5

T₅₀ = 9 + 245

T₅₀ = 254

How to determine the difference

  • 50th term (T₅₀) = 254
  • 10th term (T₁₀) = 54
  • Difference =?

Difference = T₅₀ – T₁₀

Difference = 254 – 54

Difference = 200

Learn more about arithmetic sequence:

https://brainly.com/question/16130064

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