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Lisa Cooper

Answered question

2022-04-09

Use the approach in Gauss's Problem and find the following sums of arithmetic sequences.

293 + 290 + 287 + 284 + . . + 2

ditumpasz9xj

Beginner2022-04-10Added 8 answers

Gauss's approach:
Consider the given sequence

a_{1} + a_{2} + a_{3} + \dots a_{n - 2} + a_{n - 1} + a_{n}

Pair up the terms as

a_{1} + a_{n}, a_{2} + a_{n - 1}, a_{3} + a_{n - 2}, \dots

Each pairwise sum in the sequence will be the same aand there are

\frac{n}{2}

such pairs
Thus, we get

\frac{n}{2} \times (a_{1} + a_{n})

Hence,

a_{1} + a_{2} + a_{3} + \dots a_{n - 2} + a_{n - 1} + a_{n} = \frac{n}{2} \times (a_{1} + a_{n})

The common difference of the terms of the sequence is

d = 290 - 293 = - 3

To find n use the formula

a_{n} = a_{1} + (n - 1) d

2 = 293 + (n - 1) (- 3)

n - 1 = \frac{- 291}{- 3}

n = 98

Therefore, the sum of the sequence is

\frac{n}{2} \times (a_{1} + a_{n}) = \frac{98}{2} \times (293 + 2) = 14455

tralhavahr9c

Beginner2022-04-11Added 16 answers

Thanks

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