That's an arithmetic sequence. To find the rule of the sequence, we need to find the first term (a₁) and the difference of the sequence (d)
Make an equation system based on what are given by the question.
an = a₁ + d(n - 1)
a₆ = a₁ + d(6 - 1) = -8
a₆ = a₁ + 5d = -8 (first equation)
a₁₅ = a₁ + d(15 - 1) = -62
a₁₅ = a₁ + 14d = -62 (second equation)
Solve the equation to find the value of a₁ and d
Using elimination method, find the value of d from first equation and second equation
a₁ + 14d = -62
a₁ + 5d = -8
-------------------- - (substract)
9d = -54
d = -54/9
d = -6
Using subtitution method, find the value of a₁. Subtitute d with -6 from the first equation.
a₁ + 5d = -8
a₁ + 5(-6) = -8
a₁ - 30 = -8
a₁ = -8 + 30
a₁ = 22
Determine the rule of the sequence
General rule for arithmetic sequence is
an = a + d(n - 1)
Now input the value of a₁ and d to the general rule, then simpllify.
an = a + d(n - 1)
an = 22 + -6(n - 1)
an = 22 -6n + 6
an = 28 - 6n
The rule of the sequence is 28 - 6n
