ExpertMedium1 markShort Answer
AQA GCSE · Question 23.1 · Algebra
The first three terms of a geometric progression are √5/2, 5/4, 5√5/8. Work out the next term.
The first three terms of a geometric progression are √5/2, 5/4, 5√5/8. Work out the next term.
How to approach this question
1. First, find the common ratio (r) of the geometric progression. You can do this by dividing the second term by the first term.
2. Remember that to divide by a fraction, you multiply by its reciprocal.
3. You may need to rationalise the denominator to simplify the common ratio.
4. Once you have the common ratio, multiply the third term by it to find the fourth term.
Full Answer
A geometric progression is a sequence where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
1. **Find the common ratio (r):**
r = (Term 2) / (Term 1)
r = (5/4) / (√5/2)
To divide by a fraction, we multiply by its reciprocal:
r = (5/4) × (2/√5)
r = 10 / (4√5) = 5 / (2√5)
To simplify this, we can write 5 as (√5)².
r = (√5)² / (2√5) = √5 / 2.
Let's check this with Term 3 / Term 2:
r = (5√5/8) / (5/4) = (5√5/8) × (4/5) = (20√5) / 40 = √5 / 2.
The common ratio is indeed r = √5 / 2.
2. **Find the next term (Term 4):**
Term 4 = Term 3 × r
Term 4 = (5√5 / 8) × (√5 / 2)
Term 4 = (5 × √5 × √5) / (8 × 2)
Since √5 × √5 = 5:
Term 4 = (5 × 5) / 16
Term 4 = 25 / 16.
Common mistakes
✗ Errors in dividing fractions.
✗ Errors when working with surds, especially rationalising the denominator or multiplying surds.
✗ Arithmetic mistakes.
Practice the full AQA GCSE Maths Higher Tier Paper 1 Non-Calculator
32 questions · hints · full answers · grading
More questions from this exam
Q01Work out 12² ÷ (1/3 × √36)EasyQ02Measure the shortest distance from point P to the line. Give your answer in millimetres.EasyQ03The vector (<sup>-3</sup><sub>7</sub>) translates A to B. Write down the vector that translates B...EasyQ04.1The attendance for a rugby match is 8400 people to the nearest 100.
Write down the minimum possib...EasyQ04.2Write down the maximum possible attendance.Easy