Question

Write an equation fo nth term of the given arithmetic sequence 7,13,19,25,...

Answer 1

Explanation:

7, 13, 19, 25, .......

Arithmetic sequence.

First term = a = 7

Common difference = d = second term - first term

d = 13 - 7 = 6

nth term
`a_(n)=a+(n-1)d\\`

`a_(n) = 7 +(n-1)*6\\\\\\a_(n)=7 + 6n - 6\\\\\\a_(n) = 1 + 6n`

Answer 2

The nth term for the given sequence can be written as:

`a_n=6\,n+1`

Explanation:

Notice that this arithmetic sequence is created by adding to each term a common difference of 6 units:

7 + 6 = 13

13 + 6 = 19

19 + 6 = 25

Then, using the general expression for the nth term of an arithmetic sequence of first term "
`a_1`" and common difference "d" we can write the nth term as:

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

which in this case translates as:

`a_n=a_1+(n-1)\,d= 7\,+(n-1)\,6=7+6\,n-6=6\,n+1`