Here are the first five terms of an arithmetic sequence. 7 13 19 25 31 (a) Find an expression, in terms of n, for the nth term of this sequence. The nth term of a different sequence is 8 - 6n (b) Is -58 a term of this sequence? You must show how you get your answer.

GCSE Edexcel Maths Sequences: Here are the first five terms of

Here are the first five terms of an arithmetic sequence - Edexcel - GCSE Maths - Question 3 - 2022 - Paper 2

Question 3

Here are the first five terms of an arithmetic sequence. 7 13 19 25 31 (a) Find an expression, in terms of n, for the nth term of this sequence. The n... show full transcript

Worked Solution & Example Answer:Here are the first five terms of an arithmetic sequence - Edexcel - GCSE Maths - Question 3 - 2022 - Paper 2

Step 1

Find an expression, in terms of n, for the nth term of this sequence.

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Answer

The first step is to identify the common difference in the arithmetic sequence. The sequence is 7, 13, 19, 25, 31, where the common difference can be calculated as follows:

Common difference = 13 - 7 = 6.

Now, we can express the nth term ( T_n) of the sequence using the formula:

$T_n = a + (n-1)d$

where:

a is the first term (7 in this case), and
d is the common difference (6).

Substituting the values we have:

$T_n = 7 + (n-1) imes 6$

Simplifying this gives:

$T_n = 7 + 6n - 6 = 6n + 1$

Thus, the expression for the nth term is: $T_n = 6n + 1$

Step 2

Is -58 a term of this sequence?

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Answer

To determine if -58 is a term of the sequence, we set the nth term equal to -58 and solve for n:

$6n + 1 = -58$

Subtracting 1 from both sides gives:

$6n = -59$

Dividing by 6 results in:

$n = -\frac{59}{6}$

Since n must be a positive integer, -58 is not a term of the arithmetic sequence. Therefore, -58 is not a term of this sequence.

Here are the first five terms of an arithmetic sequence - Edexcel - GCSE Maths - Question 3 - 2022 - Paper 2

Worked Solution & Example Answer:Here are the first five terms of an arithmetic sequence - Edexcel - GCSE Maths - Question 3 - 2022 - Paper 2

Find an expression, in terms of n, for the nth term of this sequence.

Is -58 a term of this sequence?

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