arithmetic sequence

Question

find a formula for the nth term of the arithmetic sequence

first term: 2.5

common difference: -0.2

Answer 1

There is a general formula which I can give you, but I would also encourage an intuitive approach.

We'll start small. The first term is 2.5. That's the starting point before any adding happens.

Ten term 2 is 2.5 + -0.2, which is 2.3. The second term resulted from adding the common difference 1 time.

Term 3 comes from adding -0.2 (the common difference) again, for a total of 2 times.

We've already gone far enough to establish the pattern that the common difference gets added 1 less time than the current term number. So the 50th term would result from adding -0.2 49 times because it is 49 terms after the first one.

This suggests the formula a_n = a₁ + d(n - 1).

We put in the values we know, and we have a_n = 2.5 + (n - 1)*(-0 2). If it requires further simplification, then I'll leave you to do that.

Answer 2

formula for nth term is

a_n= a₁+(n-1)*d

=> a_n= 2.5 + (n-1)*(-0.2)

=>a_n= 2.5-0.2n +0.2

=> a_n= 2.7 - 0.2n