$625 Andrew will earn over the course of 10 weeks.
It is given that Andrew earns an allowance of $4 the first week, $17 the next week, $30 and so on.
It is required to find how much will Andrew earn over the course of 10 weeks.
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
This is the question of an arithmetic sequence, the sequence is:
4, 17, 30,......
Here first term a = 4
and common difference d = 17-4 ⇒13
The sum of the arithmetic sequence for the number of 10th terms.
[tex]\rm S_n=\frac{n}{2} [2a+(n-1)d][/tex]
[tex]\rm S_n=[/tex] The sum of the arithmetic sequence
Number of terms n = 10
Putting the above values in the formula, we get:
[tex]\rm S_n=\frac{10}{2} [2\times4+(10-1)\times13][/tex]
[tex]\rm S_1_0=5[8+9\times13]\\\\\rm S_1_0=5[125]\\\\\rm S_1_0 = 625[/tex]
Thus, the $625 Andrew will earn over the course of 10 weeks.
Learn more about the sequence here:
brainly.com/question/21961097
