Photo AI

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 nth term ... 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.

96%

114 rated

Answer

The given terms form an arithmetic sequence. The first term (a) is 7 and the common difference (d) is found by subtracting the first term from the second term:

$d = 13 - 7 = 6$

The nth term of an arithmetic sequence can be expressed as:

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

Substituting the values of a and d:

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

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?

99%

104 rated

Answer

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

$6n + 1 = -58$

Subtracting 1 from both sides:

$6n = -59$

Dividing both sides by 6 gives:

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

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

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;