If X+6, 2x+1, 4x-13,... Form An Arithmetic Sequence Find The 5th Term. (Show Your Solution).

If x+6, 2x+1, 4x-13,... Form an arithmetic sequence find the 5th term. (Show your solution).

 

Answer:

The fifth term (a₅) is 31.

Step-by-step explanation:

Given:

a₁ = x+6

a₂ = 2x+1

a₃ = 4x-13

Find the value of x:

a₂ - a₁ = a₃ - a₂   ⇒  common difference formula

2x+1 - (x+6) = 4x-13 - (2x+1)

2x + 1 - x - 6 = 4x - 13 - 2x - 1

2x - x - 4x + 2x = -13 - 1 - 1 + 6

-x = -9

x = 9

The sequence:

a₁ = x+6 ⇒  9=6 = 15

a₂ = 2x+1  ⇒  2(9)+1 = 19

a₃ = 4x-13  ⇒  4(9)-13 = 23

The sequence is: 15, 19, 23

The common difference (d) is 4.

Find the 5th term:

n = 5

a₁ = 15

an = a₁ + (n-1)(d)  ⇒  General Rule

a₅ = 15 + (5-1)(4)

a₅ = 15 + 16

a₅ = 31

The fifth term (a₅) is 31.


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