Question

Formula for an for the arithmetic sequence.
ah = -1, d = -7

Answer 1

The formula for the arithmetic sequence will be:

• 
  `a_n=-7n+6`

Explanation:

Given

• a₁ = -1

• d = -7

• We know that we can get the next term of the Arithmetic sequence by taking the current term and adding the common difference.

so

a₂ = a₁ + d

= -1 + (-7) ∵ a₁ = -1

= -1 - 7

= -8

similarly,

a₃ = a₂ + d

= -8 + (-7)

= -8 - 7

= -15

and so on

Thus, the Arithmetic sequence becomes

a₁, a₂, a₃, ...

-1, -8, -15, ...

as

• a₁ = -1

• d = -7

Therefore, An arithmetic sequence has a constant difference d and is defined by

`a_n=a_1+\left(n-1\right)d`

substituting a₁ = -1 and d = -7

`a_n=-7\left(n-1\right)-1`

`a_n=-7n+6`

Hence, the formula for the arithmetic sequence will be:

• 
  `a_n=-7n+6`