Question

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

Answer 1

Partial sum up to `25` th term is `375`

Explanation:

1 st term is `a= 75` Common difference is `b= 70-75= -5` No. of terms `n=25 ; 25` th term is

`T_25 = a + (n-1) * b = 75 + (25-1) * (-5) = -45`

Partial sum up to `25` th term is `S_25 =n/2{ 2a+(n-1)b}` or

`S_25 =25/2{ 2*75+(25-1)* (-5)} = 25/2 { 150 -120} =25/2*30 =25*15= 375 :. S_25= 375`
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