# How do you find the 25th partial sum of the arithmetic sequence #75, 70, 65, 60,...#?

Partial sum up to

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To find the 25th partial sum of the arithmetic sequence 75, 70, 65, 60,..., you can use the formula for the nth term of an arithmetic sequence, which is ( a_n = a_1 + (n-1)d ), where ( a_n ) is the nth term, ( a_1 ) is the first term, n is the term number, and d is the common difference.

In this sequence, the first term ( a_1 ) is 75, and the common difference d is -5 (since each term decreases by 5). Now you can use the formula to find the 25th term:

( a_{25} = 75 + (25-1)(-5) ) ( a_{25} = 75 + 24(-5) ) ( a_{25} = 75 - 120 ) ( a_{25} = -45 )

Therefore, the 25th term of the sequence is -45.

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