Question

(a) Write an expression, in terms of n, for the nth term of this sequence.

-1,3,7,11

Answer 1

The expression for nth term is:

a_n = -5+4n

Further explanation:

Given sequence is:

-1,3,7,11

We have to determine first if this is a arithmetic sequence or geometric sequence

The sequence is an arithemtic sequence if the common difference of cosecutive terms is same.

In this case,

$d = a_2 -a_1 = 3-(-1) = 3+1 = 4\\a_3 -a_2 = 7-3 = 4$

As the common difference is same the sequence is an arithmetic sequence

Standard form of arithmetic sequence is:

$a_n = a_1+(n-1)d$

Putting the values of a_1 and d

$a_n = -1 + (n-1)(4)\\a_n = -1+4n-4\\a_n = -5+4n$

The expression for nth term is:

a_n = -5+4n

Keywords: Arithmetic Sequence, nth term

Learn more about arithmetic sequence at:

• brainly.com/question/4282963
• brainly.com/question/4109519

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