Question

Chris’ Cafe is increasing its customer base by advertising. On the first day of the campaign, they had 3 customers. On the second, they had 11, and on the third, they had 19. Is the sequence that represents the number of customers arithmetic? If it is, write the recursive formula for the sequence.

Answer 1

The sequence that represents the number of customers is arithmetic, and the recursive formula is $T_n = T_{n-1} + 8$

The number of customers on the first day is represented as:

$T_1 = 3$

The number of customers on the second day is represented as:

$T_2 = 11$

The number of customers on the third day is represented as:

$T_3 = 19$

So, we have:

$T_1 = 3$

$T_2 = 11$

$T_3 = 19$

Rewrite the above sequence as:

$T_1 = 3$

$T_2 =3 + 8$

$T_3 =11 + 8$

So, we have:

$T_1 = 3$

$T_2 = T_1 + 8$

$T_3 = T_2 + 8$

Express 2 as 3 - 1

$T_3 = T_{3-1} + 8$

Substitute n for 3

$T_n = T_{n-1} + 8$

Hence, the sequence represents an arithmetic pattern, and the recursive formula is $T_n = T_{n-1} + 8$

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