What is the sum of the arithmetic sequence 174, 168, 162 …, if there are 35 terms?

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Answer 1 · 2018-06-19T08:48:12

#color(orange)(S_(35) = 2520)#

#"sum of n terms of an A.S. " = S_n = (n/2) [2a + (n-1)d]#

#a = 174, n = 35, d = 168 - 174 = 162 - 168 =- 6#

Substituting for a, d, n in the formula,

#S_(35) = (35/2) * [(2* 174) + (35-1)*(-6)]#

#S_(35) = (35/2) [348 - 204] = (35/2) * 144 = 2520#

Answer 2 · 2018-06-19T08:53:58

#color(orange)(S_(35) = (35/2)(a + a_(35)) = 2520#

#n^(th) " term of an Arithmetic Sequence "#a_n = a + (n-1) d#

#a = 174, a_2 = 168, a_3 = 162, d = 166 - 174 = -6, n = 35#

#a_(35) = 174 + (35-1) * (-6) = 174 - 204 = - 30#

#"Sum of 35 terms " = S_(35) = (n/2)(a + a_(35)) #

#S_(35) = (35/2)(174 + (-30)) = 35 * 72 = 2520#