The first four terms of a sequence are given. Can these terms be the terms of an arithmetic sequence?ln(2), ln(4), ln(8), ln(16), Yes, the sequence is arithmetic.No, the sequence is not arithmetic. If the sequence is arithmetic, find the common difference d. (If the sequence is not arithmetic, enter DNE.)d =
Question
The first four terms of a sequence are given. Can these terms be the terms of an arithmetic sequence?ln(2), ln(4), ln(8), ln(16), Yes, the sequence is arithmetic.No, the sequence is not arithmetic. If the sequence is arithmetic, find the common difference d. (If the sequence is not arithmetic, enter DNE.)d =
Solution
To determine if a sequence is arithmetic, we need to check if the difference between consecutive terms is constant.
The given sequence is ln(2), ln(4), ln(8), ln(16).
Let's find the difference between the consecutive terms:
ln(4) - ln(2) = ln(4/2) = ln(2) ln(8) - ln(4) = ln(8/4) = ln(2) ln(16) - ln(8) = ln(16/8) = ln(2)
As we can see, the difference between each pair of consecutive terms is constant and equal to ln(2). Therefore, the sequence is arithmetic.
The common difference d of an arithmetic sequence is the difference between any two successive members. In this case, d = ln(2).
Similar Questions
In an arithmetic sequence, the first term is 2 and the second term is 5.(a) Find the common difference. [2](b) Find the eighth term. [2](c) Find the sum of the first eight terms of the sequence.
Find the first five terms of the sequence.an = 7 + 2na1 = a2 = a3 = a4 = a5 = Determine whether the sequence is arithmetic. If it is arithmetic, find the common difference d. (If the sequence is not arithmetic, enter DNE.)d = Express the nth term of the sequence in the standard form an = a + (n − 1)d. (If the sequence is not arithmetic, enter DNE.)
The nth term of an arithmetic sequence is given.an = 72 − (n − 1)(a) Find the first five terms of the sequence.a1= a2= a3= a4= a5= (b) What is the common difference d?d = (c) Graph the terms you found in (a).
A sequence is such that, the difference between successive terms form an arithmetic progression, then its nth term is given by:
The first four terms of a sequence are given. Determine whether these terms can be the terms of an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic or geometric, find the next term.(a) 9, −9, 9, −9, arithmeticgeometric neither arithmetic or geometricIf the sequence is arithmetic or geometric, find the next term. (If the sequence is neither, enter DNE.) (b) 5, 35, 65, 1, arithmeticgeometric neither arithmetic or geometricIf the sequence is arithmetic or geometric, find the next term. (If the sequence is neither, enter DNE.) (c) 2, −1, 12, 2, arithmeticgeometric neither arithmetic or geometricIf the sequence is arithmetic or geometric, find the next term. (If the sequence is neither, enter DNE.) (d) x − 1, x, x + 1, x + 2, arithmeticgeometric neither arithmetic or geometricIf the sequence is arithmetic or geometric, find the next term. (If the sequence is neither, enter DNE.)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.