Question

Write an equation for the nth term of the arithmetic seqeuence.

a. 100,110,120,130...​

Answer 1

The equation for the nth term of the arithmetic sequence is 10n + 90.

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the difference is 10, so the common difference is 10. The first term of the sequence is 100. We can use the formula for the nth term of an arithmetic sequence to find the equation:

{{a_n = a_1 + (n-1)d}}

where:

• {{a_n}} is the nth term of the sequence
• {{a_1}} is the first term of the sequence (100)
• {{d}} is the common difference (10)
• {{n}} is the position of the term we want to find

Substituting the values into the formula, we get:

{{a_n = 100 + (n - 1) imes 10}}

Therefore, the equation for the nth term of the arithmetic sequence is {{100 + 10n - 10 = 10n + 90}}.