You finally get an allowance . You put $2 away in January, 4$ away in February, $8 away in March, $16 away in April and followed this saving pattern through to December. How much money do you have in 12 months? Please explain
Chelle's solution gives the 12th term, but does not show the sum of all 12 terms, which was what was asked.
yeah 8190 dumbos
i got 8190 thank you
2+4+8+...+2^n = 2^(n+1)-2
To find out how much money you have in 12 months, we need to identify the pattern in the savings and calculate the total.
The savings pattern follows a doubling sequence. Each month, the amount saved is double the previous month's savings. Starting with $2 in January, the savings are as follows:
January: $2
February: $4 (double of $2)
March: $8 (double of $4)
April: $16 (double of $8)
May: $32 (double of $16)
June: $64 (double of $32)
July: $128 (double of $64)
August: $256 (double of $128)
September: $512 (double of $256)
October: $1,024 (double of $512)
November: $2,048 (double of $1,024)
December: $4,096 (double of $2,048)
To calculate the total amount saved over 12 months, we add up all the savings:
$2 + $4 + $8 + $16 + $32 + $64 + $128 + $256 + $512 + $1,024 + $2,048 + $4,096 = $8,190
Therefore, you will have $8,190 in total after 12 months of following this saving pattern.
The answer is 2+4+8+16 = 60. That’s the answer
2,4,8,16,......
This is a geometric sequence. That means the same number is multiplied, which is 2.
You could calculate this way;
{a, ar, ar^2, ar^3, ar^4, …..}
2, 2x2 2x2^2 2x2^3 2x2^4
(2, 4, 8, 16, 32, ...)
a = the 1st term.
common ratio = 2 > the factor between terms.
Formula:
an = ar^(n - 1)
an = 2 x 2^(n – 1)
a = 2 > 1st term
r = 2 > common ratio
n = nth term > the term you're going to.
The third and fourth term you already know.
a(3)= 2 x 2^(3 - 1)
a(3)= 2 x 2^2
a(3)= 2 x 4
a(3) = $8
a(4)= 2 x 2^(4 - 1)
a(4)= 2 x 2^3
a(4)= 2 x 8
a(4)= $16
a(12)= 2 x 2^(12 - 1)
a(12)= 2 x 2^11
a(12)= 2 x 2048
a(12)= %4096
Answer:
$4096