aag arithmetic sequences

Question

Common difference: 8

Third term: 6

What is the 6th term?

Also

4, 5 1/3, 6 2/3

Determine the numerical position of the term 24

Answer 1

a_n = a₁ + (n-1)d

a₃ = a₁ + 2(8) = 6 So, a₁ = -10

a₆ = -10 + 5(8) = 30

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a_n = 4 + (4/3)(n - 1) = 24

Solve for n.

Answer 2

a3 =6

d=8

a3 = a1 +8(2) = 6

a1 =6-16 =-10

a6=-10+8(5)

a6 = 30 = 6th term

-10,-2,6,14,22,30...

4, 5 1/3, 6 2/3

d = 1 1/3

an=a1 +d(n-1)

an = 4 + (4/3)(n-1)

a24 = 4 +(4/3)(23)

= 4 +92/3 =12/3+92/3

=104/3 = 34 2/3 = 24th term