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

Question

1611 views around the world

You can reuse this answer
Creative Commons License

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#