Question

Find the 66th
term in the following
arithmetic sequence
-92, -85, -78, -71, ...

Answer 1

The
`66`th term is
`363`.

Explanation:

To find the
`n`th term, the formula is
`7n - 99`. Since we want to find the
`66`th term, we can plug
`n` for
`66`. So our expression is now
`7 \cdot 66 - 99 =`
`66`th term. Solving this we have

`462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\`. Therefore, the
`66`th term is
`\boxed{363}`.

Answer 2

a₆₆ = 363

Explanation:

the nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then

a₆₆ = - 92 + (65 × 7)

= - 92 + 455

= 363