Question on sequences!!

[abhishekswamy]

In an arithmetic sequence T1,T2,T3..Tn..., T1=23 and Tn=Tn-1 - 3 for each n>1 what is the value of n where Tn =-4

a.)-1
b.)7
c.)10
d.)14
e.)20

[Anurag@Gurome]

In an arithmetic sequence T1,T2,T3..Tn..., T1=23 and Tn=Tn-1 - 3 for each n>1 what is the value of n where Tn =-4

T(1) = 23 and T(n) = T(n - 1) - 3 for each n > 1

Hence, the series is an arithmetic progression with first term, a = 23 and common difference, d = -3.

Hence, T(n) = a + (n - 1)d = 23 + (n - 1)*(-3) = 23 - 3n + 3 = 26 - 3n

Given that, T(n) = -4
--> (26 - 3n) = -4
--> 3n = 30
--> n = 10

The correct answer is C.