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calculates the sum of the first 8 terms of an arithmetic progression starting with 3/5 and ending with 1/4

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We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

How to get the sum of the first 8 terms?

In an arithmetic sequence, the difference between any two consecutive terms is a constant.

Here we know that:

[tex]a_1 = 3/5\\a_8 = 1/4[/tex]

There are 7 times the common difference between these two values, so if d is the common difference:

[tex]a_1 + 7*d = a_8\\\\3/5 + 7*d = 1/4\\\\7*d = 1/4 - 3/5 = (5 - 12)/20 = -7/20\\\\d = -1/20[/tex]

Then the sum of the first 8 terms is given by:

[tex]3/5 + (3/5 - 1/20) + (3/5 - 2/20) + ... + (3/5 - 7/20)\\\\8*(3/5) - (1/20)*(1 + 2 + 3+ 4 + 5 + 6 + 7) = 3.4 = 34/10 = 17/5[/tex]

So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.

If you want to learn more about arithmetic sequences:

https://brainly.com/question/6561461

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