1. what is the possible value
2. what is the sum of the finite arithmetic series

10. A possible value of missing term is -175 ⇒ last answer

11. The sum = 900 ⇒ first answer

Step-by-step explanation:

10. ∵ It is a geometric sequence

∴ The constant ratio between any two consecutive numbers is r

∴ r = x/35 and r = 875/x ⇒ x is the missing term

∴ x/35 = 875/x

∴ x² = (35)(875) = 30625

∴ x = ±√30625 = ± 175

∴ A possible value of missing term is -175

11. ∵ -10 , 0 , 10 , 20 , , 130 is arithmetic series

∴ Tn = a + (n - 1)d

  a is the first term , d difference between any 2 consecutive terms

  n is the position of the number in the series

∴ Sn = n/2(a + L) ⇒ L is the last term

∵ a = -10 , d = 10 , L = 130

∴ 130 = -10 + (n - 1)(10)

∴ 130 + 10 = 10(n - 1) ⇒ 140 = 10(n - 1)

∴ 140/10 = n - 1 ⇒ 14 = n - 1 ⇒ n = 14 + 1

∴ n = 15

∴ S(15) = 15/2 [-10 + 130] = 15/2 (120) = 900