Question

Write an equation for the nth term of the arithmetic seqeuence. The
-6, -9, -12, -15, ...

Answer 1

The nth term of the given sequence is given by a(n) = -3(1 + n)

Explanation:

The given AP sequence is -6, -9, -12, -15, ...

Here, the first term = -6

The common difference (d) = a 2 - a 1

= -9 - (-6) = -9 + 6

= -3

⇒ d = - 3

Now, nth term of the Arithmetic Sequence is
`a_n  = a+ (n-1)d`

⇒ a(n) = -6 + (n-1) (-3)

= -6 -3n + 3

= -3 - 3n

or, a(n) = -3(1 + n)

Hence, the nth term of the given sequence is given by a(n) = -3(1 + n)