CAIE A-Level Mathematics AS 1.6.3 Progression Formulae Questions

Practise using nth-term and sum formulae for arithmetic and geometric progressions and forming linked equations when terms or partial sums create a second progression.

Exam points

Use the nth-term formula and the finite-sum formula for arithmetic progressions to determine terms, common differences or sums from given conditions.
Use the nth-term and finite-sum formulae for geometric progressions to calculate terms or sums from stated information.
Translate conditions on terms or sums into equations to determine unknowns, including testing whether given numbers or terms form an arithmetic or geometric progression.

[Maximum number: 7]

The first term of an arithmetic progression is 1.5 and the sum of the first ten terms is 127.5 .

(a)

Find the common difference.

[ 2 ]

(b)

Find the sum of all the terms of the arithmetic progression whose values are between 25 and 100 .

[ 5 ]

Attempt to find either the first term or the last term in the set by considering
1.5+2.5(n-1)>25 or 1.5+2.5(n-1)<100 or equivalent equations
Using their d.
May be implied by correct answers.

State or imply that 11th term or 26.5 is the first in the set
State or imply that 40th term or 99 is the last in the set
Either use $S_{40}-S_{10}$

Or use $\frac{1}{2} n(a+l)$ with correct results for their d Or use $\frac{1}{2} n[2 a+(n-1) d]$ with correct results for their d
Their 40 and 10 from correct working with their
d.
Correct values 30, 26.5 and 99 respectively.
Correct values 30, 26.5 and 2.5 respectively.

Obtain 1882.5
OE

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CAIE A-Level Mathematics AS 1.6.3 Progression Formulae Questions question 1

Question (a)

Question (b)