Marcus was giving dollar bills from his grandfather each day for one week. On the first day he received one dollar, on the second day he received two dollars, on the third day he received four dollars, and on the fourth day he received eight dollars. If this pattern continues, how much money will Marcus have by the end of the week

Marcus will make $127 by the end of the month.

Step-by-step explanation:

On the first day he received one dollar, on the second day he received two dollars, on the third day he received four dollars, and on the fourth day he received eight dollars. This means that the amount of money he receives is increasing in a geometric progression.

The sum of n terms of a sequence is expressed as

Sn = a (r^n - 1) / (r - 1)

Where

a is the first term of the sequence

r is the common ratio,

n is the number of terms.

From the information given,

n = 7 (a week is 7 days)

a = 1 (amount for the first day)

r = 2

S7 = 1 (2^7 - 1) / (2-1)

S7 = 128 - 1 = 127