math precalculus 12

Question

Helmut's parents gave him $1 on his first birthday (which went into his brand new piggy bank). On his second day, he received $3 and on his third birthday $5. His parents continued to give him money following an arithmetic sequence. How much money would he have in total, in his piggy bank, on his 13th birthday?

Answer 1

Looks like an odd number sequence: 1, 3, 5, ....

a_n = 2n-1

a₁₃ = 2(13)-1 = 26-1 = $25

There is a neat formula for the sum of odd numbers:

∑a_n = ∑(2n-1) = n²

So if Helmut had saved all his birthday money for 13 years, He would have 13² = $169