If An = 1/2 a(n-1) + 4 and a = 6, find the fifth term of the sequence. Express the answer as a fraction and as a decimal

I think its n = 7

Reorder the terms:

6(-1 + n) = 2(2n + 4)

(-1 * 6 + n * 6) = 2(2n + 4)

(-6 + 6n) = 2(2n + 4)

Reorder the terms:

-6 + 6n = 2(4 + 2n)

-6 + 6n = (4 * 2 + 2n * 2)

-6 + 6n = (8 + 4n)

Solving

-6 + 6n = 8 + 4n

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-4n' to each side of the equation.

-6 + 6n + -4n = 8 + 4n + -4n

Combine like terms: 6n + -4n = 2n

-6 + 2n = 8 + 4n + -4n

Combine like terms: 4n + -4n = 0

-6 + 2n = 8 + 0

-6 + 2n = 8

Add '6' to each side of the equation.

-6 + 6 + 2n = 8 + 6

Combine like terms: -6 + 6 = 0

0 + 2n = 8 + 6

2n = 8 + 6

Combine like terms: 8 + 6 = 14

2n = 14

Divide each side by '2'.

n = 7

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step-by-step explanation: