The total size of the spam folder is 25,450 KB.
The sequence provided follows an arithmetic progression where each term increases by 5.
To find the total size of the spam folder, use the formula for the sum of an arithmetic series:
Sn = n/2 × (2a + (n-1)d)
where:
Sn is the sum of the series.
n is the number of terms.
a is the first term.
d is the common difference between terms.
Given:
n = 100 (number of emails),
a = 7 (size of the first email),
d = 5 (common difference).
S¹⁰⁰ = 100/2 × (2 × 7 + (100-1) × 5)
S¹⁰⁰ = 50 × (14 + (99 × 5)
S¹⁰⁰ = 50 × (14 + 495)
S¹⁰⁰ = 50 × 509)
S¹⁰⁰ = 25450
Therefore, the total size of the spam folder is 25,450 KB.