Question

How do you find the 10th partial sum of the arithmetic sequence `40, 37, 34, 31,...`?

Answer 1

`10` th partial sum is `265`

Explanation:

`S : {40 , 37 ,34,31 ...}`

First term is `a_1=40` , common difference is `d=37-40=-3`

and number of terms `n=10`

Sum of `n` terms is `S_n = n/2{2 a_1+(n-1)d}`

`:. S_10 = 10/2{2*40+(10-1)* (-3)}` or

`S_10 = 5(80-27)= 5 * 53= 265`

`10` th partial sum is `265` [Ans]

Answer 2

`color(maroon)(S_(10) = 265`

Explanation:

Arithmetic sequence `40, 37, 34, 31, . . .`

First term `a = 40`

Common difference `d = 37 - 40 = 34 - 37 = 31 - 34 = -3`

`n^(th) term = a_n = a + (n-1) * d`

`a_(10) = a + (10-1) * d = 40 + 9 * -3 = 40 - 27 = 13`

Sum of first n terms `S_n =n/2 * (a + a_n)`

`S_(10) = 10/2 * (a + a_(10)) = 5 * (40 + 13) = 265`