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

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Answer 1 · 2018-08-05T10:41:40

#10# th partial sum is #265#

#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 · 2018-08-05T12:59:29

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

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#