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

Given the sequence: 1, 3, 5 7, ...

Find sum when n = 13

SOLUTION:

Constant difference ==>

Arithmetic Sequence with d = 2

an = value of nth term

an = a1 + d(n-1)

an = 1 + 2(n-1)

a13 = 1 + 2(13-1)

a13 = 1 + 24 = 25 Amount given on 13th bday.

Sn = Sum of first n terms

Sn = (Average)*n

Sn = [ (first + last) /2 ]*n

Sn = [ (a1 + an)/2 ] * n

S13 = Sum of first 13 terms

S13 = [ (a1 + a13)/2 ] * 13

S13 = [ (1 + 25)/2 ] * 13

S13 = [ 26/2 ] * 13

S13 = [ 13 ] * 13

S13 = 169

Total amount after 13 birthday gifts is $169