Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 9, 10, 11, 12, ...

Answer 1

`T_n= 9+(n-1)`

Explanation:

The Given sequence is 9, 10, 11, 12

We need to find the expression to describe the sequence.

Let
`T_n` be the
`n^(th)` term of the sequence.

Let n represent the position of the term.

Let a be the first term in the sequence.

and d be the common difference between the sequence

Hence the expression to find the above sequence is given below;

`T_n= a+(n-1)d`

when n=1 d= 1 a = 9

`T_1 = 9+(1-1)1 = 9 + 0 = 9`

when n=2 d= 1 a = 9

`T_2 = 9+(2-1)1 = 9 + 1 = 10`

when n=3 d= 1 a = 9

`T_3 = 9+(3-1)1 = 9 + 2 = 11`

when n=3 d= 1 a = 9

`T_4 = 9+(4-1)1 = 9 + 3 = 12`

Hence the expression is
`T_n= 9+(n-1)`