Find the 4th and 5th Terms in the Sequence 10n-9: Step-by-Step Solution

Question

10n9 10n-9

What are the fourth and fifth terms of the sequence above?

Video Solution

Solution Steps

00:00 Find elements 4,5
00:05 We'll substitute the desired element position in the sequence formula and solve
00:20 Always solve multiplication and division before addition and subtraction
00:27 This is the 4th element in the sequence
00:33 We'll use the same method to find the next element
00:37 We'll substitute the desired element position in the sequence formula and solve
00:49 Always solve multiplication and division before addition and subtraction
00:56 And this is the solution to the question

Step-by-Step Solution

The fourth and fifth terms in the sequence are the terms: a4,a5 a_4,\hspace{4pt}a_5 meaning in the general term formula given:

an=10n9 a_n=10n-9 we need to substitute the position (of the requested term in the sequence):

n=4 n=4 for - a4 a_4 and-

n=5 n=5 for-

a5 a_5 Let's do this for the fourth term:

an=10n9n=4a4=1049=409a4=31 a_{\underline{n}}= 10\underline{n}-9 \\ n=\underline{4}\\ \downarrow\\ a_{\underline{4}}= 10\cdot\underline{4}-9=40-9\\ a_4=31 when we substituted in place of n the position (of the requested term in the sequence): 4, substitution is shown with an underline in the expression above,

Similarly, for the fifth term, a5 a_5 we get:

a5=1059=509a5=41 a_{\underline{5}}= 10\cdot\underline{5}-9=50-9\\ a_5=41 which means that:

a4=31,a5=41 a_4=31,\hspace{4pt}a_5=41 Therefore the correct answer is answer A.

Answer

31, 41