Photo AI

Here are the first five terms of a sequence - Edexcel - GCSE Maths - Question 21 - 2019 - Paper 3

Question icon

Question 21

Here-are-the-first-five-terms-of-a-sequence-Edexcel-GCSE Maths-Question 21-2019-Paper 3.png

Here are the first five terms of a sequence. −1 0 3 8 15 Find an expression, in terms of n, for the nth term of this sequence.

Worked Solution & Example Answer:Here are the first five terms of a sequence - Edexcel - GCSE Maths - Question 21 - 2019 - Paper 3

Step 1

Identifying the sequence pattern

96%

114 rated

Answer

The first five terms are: -1, 0, 3, 8, 15. To find the pattern, we start by calculating the first differences between consecutive terms:

  • First differences:
    • 0 - (-1) = 1
    • 3 - 0 = 3
    • 8 - 3 = 5
    • 15 - 8 = 7

This gives us the first differences: 1, 3, 5, 7. Next, we calculate the second differences:

  • Second differences:
    • 3 - 1 = 2
    • 5 - 3 = 2
    • 7 - 5 = 2

Since the second differences are constant, we can conclude that the sequence is quadratic.

Step 2

Formulating the expression

99%

104 rated

Answer

Given that the sequence is quadratic, we can express the nth term as:

an=an2+bn+ca_n = an^2 + bn + c

Using the values of n and a_n from the first terms:

  • For n = 1, a_1 = -1: a(12)+b(1)+c=−1a(1^2) + b(1) + c = -1
  • For n = 2, a_2 = 0: a(22)+b(2)+c=0a(2^2) + b(2) + c = 0
  • For n = 3, a_3 = 3: a(32)+b(3)+c=3a(3^2) + b(3) + c = 3

Solving these equations leads to the expression:

an=n2−2n−1a_n = n^2 - 2n - 1

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

;