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

Use the formula for sum of an arithmetic sequence: S_n = (n/2)(a₁ + a_n) , where n is the # of terms, a₁ is the first term in the sum and a_n is the last.

To use this formula, you need to first calculate the 13th term: a₁₃ = 1 + 2·(13-1) = 25.

S₁₃ = (13/2)(1 + 25) = $169