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Sequences and series q

A sequence begins:

1 3 5 3 1 3 5 3 1 3

the 55th term is 5, find the sum of the first 55 terms.

I got:
sum of the first 10 terms: 28 found by adding the first 10 terms together
sum of the first 50 terms: 28 x 5 = 140
sum of the 51, 52, 53, 54, 55 terms is 5 + 3 + 1 + 3 + 5 = 17
140 + 17 = 157 BUT the answer is 165, why?

Reply 1

hello calum

Original post by Magenta96

A sequence begins:

\displaystyle\underbrace{1 3 5 3 +\cdots}_{13\text{ times}} 1 3 5

the 55th term is 5, find the sum of the first 55 terms.

the answer is 165, why?

The sequence in in 4's, So if you take 1,3,5,3 as the repeated group of 4. then in 55 terms you have 13 groups and 3/4 of a group (55/4 = 13.75).

So:

1+3+5+3 = 12

12 \times 13 = 156

So you end with

156 + 1 + 3 + 5 = 165

make sense? :smile:

(edited 11 years ago)

Reply 2

Magenta96

Original post by hello calum

The sequence in in 4's, So if you take 1,3,5,3 as the repeated group of 4. then in 55 terms you have 13 groups and 3/4 of a group (55/4 = 13.75).

So:

1+3+5+3 = 12

12 \times 13 = 156

So you end with

156 + 1 + 3 + 5 = 165

make sense? :smile:

yes, thank you :smile:

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Sequences and series q

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