Find the sum of the following series. 1 + 5 + 9 + ... + 45?

Answer 1

There are 12 terms (each term is 4n-3, for n=1 to n=12).

Pairing up the terms first+last (1+45 = 46),
second+next-to-last (5+41 = 46),
third+third-to-last (9+37), etc.,
... you'll get six pairs which each total 46.

So the answer is 6*46 = 276.

That's slightly unorthodox, but it works for any arithmetic series. The answer is the the sum of the first and last terms, times half the number of terms in the series. (Or the average of the first and last terms, times the number of terms in the series, which incorporates the "1/2" in calculating the average.)

Answer 2

1+5+9+13+17+21+25+29+33+
37+41+45 = 276

Answer 3

This is an arithmetic series where the first term is 1, the last term is 45, and 4 being added to each term. There are (45-1)/4 + 1 = 12 terns in total, so the sum is
(1/2) *12 * (1 + 45) = 276.

Answer 4

nth term = 1 + 4(n-1)

45 = 1 + 4(n-1)
n = (45 -1)/4 + 1 = 12
so sum from n = 1 to 12 of 1+ 4(n-1) or 1 + 4n - 4 or 4n - 3

4(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12) - (3 * 12)
= 4(78) - 36
= 312 - 36
= 276

Answer 5

This is arithmetic because you are adding 4 to each term to get the next. The formula is Sn = (n/2)(a1+an) where n is the number of terms, a1 is the 1st term, and an is the nth term. However, you must first find n.

45=1+(n-1)4
45=1+4n-4
48=4n
12=n

So, sum of 12 numbers = (12/2)(1+45)
sum = 276

Answer 6

I was so confused reading the answers everyone did. All you're doing is finding the missing terms. According to the pattern, you just add 4 to the next digit. Then after you do that, simply add the numbers together. You should get 276 as the sum of all the numbers together.

Answer 7

There are in all twelve terms, and if you align them pairwise by size and size reversed, you have 6 pairs which each add to 46. So the sum is 46 x 6. The stunt was invented by Gauss.

Answer 8

276

Answer 9

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