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

Answer:

$T_n= 9+(n-1)$

Step-by-step 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 $T_n= 9+(n-1)$