Question

Q6.

Here is a rule for a sequence.
After the first two terms, each term is the sum of the previous two terms.
(2) (Total 4 marks)
The first five terms are p 23 q 57 r
Work out the values of p, q and r.

Answer 1

p = 11

q = 34

r = 91

Explanation:

If each term (after the first two terms) is the sum of the previous two terms:

`\implies p+23=q`

`\implies 23+q=57`

`\implies q+57=r`

Solve the second equation for q:

`\implies 23+q=57`

`\implies 23+q-23=57-23`

`\implies q=34`

Substitute the found value of q into the first equation and solve for p:

`\implies p+23=34`

`\implies p+23-23=34-23`

`\implies p=11`

Substitute the found value of q into the third equation and solve for r:

`\implies 34+57=r`

`\implies r=91`

Therefore:

• p = 11
• q = 34
• r = 91