Find the first four terms of the sequence whose general term is given by:(a)5n+(1÷2)n_2,(b)2n+1÷3n+2
5n+(1÷2)n_2 ??? , makes no sense
b) 2n+1÷3n+2
Did you mean term(n) = (2n+1)÷(3n+2) , I will assume you did
term(1) = (2+1)/(3+2) = 3/5
term(2) = (4+1)/(6+2) = 5/8
etc
10,7,4,1,-2
To find the first four terms of a sequence, we substitute the values of n = 1, 2, 3, and 4 into the general term.
(a) For the sequence with the general term 5n + (1/2)n - 2:
Plug in n = 1:
a1 = 5(1) + (1/2)(1) - 2 = 5 + 1/2 - 2 = 3.5
Plug in n = 2:
a2 = 5(2) + (1/2)(2) - 2 = 10 + 1 - 2 = 9
Plug in n = 3:
a3 = 5(3) + (1/2)(3) - 2 = 15 + 3/2 - 2 = 14.5
Plug in n = 4:
a4 = 5(4) + (1/2)(4) - 2 = 20 + 2 - 2 = 20
Therefore, the first four terms of the sequence with the general term 5n + (1/2)n - 2 are:
a1 = 3.5, a2 = 9, a3 = 14.5, a4 = 20.
(b) For the sequence with the general term 2n + 1 ÷ 3n + 2:
Plug in n = 1:
a1 = 2(1) + 1 ÷ 3(1) + 2 = 2 + 1 ÷ 3 + 2 = 4
Plug in n = 2:
a2 = 2(2) + 1 ÷ 3(2) + 2 = 4 + 1 ÷ 6 + 2 = 6.167
Plug in n = 3:
a3 = 2(3) + 1 ÷ 3(3) + 2 = 6 + 1 ÷ 9 + 2 = 8.111
Plug in n = 4:
a4 = 2(4) + 1 ÷ 3(4) + 2 = 8 + 1 ÷ 12 + 2 = 10.083
Therefore, the first four terms of the sequence with the general term 2n + 1 ÷ 3n + 2 are:
a1 = 4, a2 = 6.167, a3 = 8.111, a4 = 10.083.