The sequence an a n 1d is an arithmetic sequence in which

The sequence. a_n = a + (n - 1)d is an arithmetic sequence in which a is the first term and d is the So for the arithmetic sequence A_n = 1 + 3(a - 1) the first term is and the common difference is True or False? If False, give a reason. If we know the first and second terms of an arithmetic sequence, then we can find any other term. True, If we know the first and second terms of an arithmetic sequence then we can find any other term. False, If we know the first and last terms of an arithmetic sequence then we can find any other term. False, If we know only the first term of an arithmetic sequence then we can find any other term. False, If we know only the second term of an arithmetic sequence then we can find any other term. False, If we know only the last term of an arithmetic sequence then we can find any other term. The nth term of an arithmetic sequence is given. a_n = -12 + 24(n - 1) Find the first five terms of the sequence. What is the common difference Graph the terms you found in part (a).

Solution

an =a + (n - 1)d

d ---> common difference

an = 1 + 3(n - 1)

By comparison,
we get a = 1 and d = 3

first term is 1 and common difference is 3

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All we need for an AP is first term and common difference

1st term and 2nd term are given
So, common diff, d = 2nd term - 1st term can be found

So, yes, any term can be found

Option A

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an = -12 + 24(n - 1)

a1 = -12
a2 = -12+24 = 12
a3 = 12 + 24 --> 36
a4 = 36 + 24 ---> 60
a5 = 60 + 24 ---> 84

Common difference, d = 24