find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. a(n) = 12 (n–1)(3) a. 0, 9, 27 b. 12, 24, 42 c. 12, 21, 39 d. 3, 24, 27
First term a=0
Fourth term= 12(4-1)3
=129
=108
10th term=12(10-1)3
=129*3
= 324
Answer:
No option suits this answer.
Step-by-step explanation:
Given is an arithmetic sequence with general term formula in n as
\(a_n = 12(n-1)+3\)
We can find any general term by substituting for n
n =1
\(a_1 = 12(1-1)(3)=0\)
I term is 0
II term is got by substituting n =2
\(a_2=12(2-1)3=36\)
Hence common difference
\(d=a_2-a_1\\d=36-0 =36\)
Hence the successive term would increase by 36
4th term
=\(a_4 =12(3)(3) =108\\a_10 = 12(9)(3) = 324\)