Find an explicit form f[n] of the arithmetic sequence for some real number x.

Question

find the value.

find the 10th term of the sequence.

Answer 1

In an arithmetic sequence each new term is found by

adding the same number to the the previous term.

This number is the common difference.

 

To find the nth term of an arithmetic sequence we

first find the common difference "d"

 

For example:  In the sequence

                     -4, 0, 4, 8, 12, ...

a₁ = -4, a₂ = 0, a₃ = 4, ....    d = 4

The common difference is 4 because each subsequent

term is found by adding 4 to the previous term.

 

To find the nth term you use the formula:

a_n = a₁ + (n-1)d

 

If I needed to find the 10th term of my above sequence

a_{10 =} a₁ + (n-1)d = -4 + (10-1)(4) = -4 + 9(4) = -4 + 36 = 32

 

Test:  we have a_{5 = 12}

the next 5 terms are 16, 20, 24, 28, 32

a₁₀ =32 as the formula figured.

 

I hope this helps.