Given that (-6, -2frac{1}{2}, …, 71) is a linear sequence , calculate the number of terms in the sequence.
-
A.
20 -
B.
21 -
C.
22 -
D.
23
Correct Answer: Option D
Explanation
(T_{n} = a + (n – 1)d) (for a linear or arithmetic progression)
Given: (T_{n} = 71, a = -6, d = -2frac{1}{2} – (-6) = 3frac{1}{2})
(implies 71 = -6 + (n – 1)times 3frac{1}{2})
(71 = -6 + 3frac{1}{2}n – 3frac{1}{2} = -9frac{1}{2} + 3frac{1}{2}n)
(71 + 9frac{1}{2} = 3frac{1}{2}n implies n = frac{80frac{1}{2}}{3frac{1}{2}})
(= 23)