CAIE IGCSE Additional Math 12.4 finite progression formulas

Use this finite-progressions page to find terms, common ratios, partial sums and the number of terms needed for a sum condition.

Exam points

Use arithmetic progression formulae to find terms, sums or the number of terms.
Use geometric progression formulae to find common ratios and nth terms.
Solve inequalities involving progression sums, such as exceeding a target total.

[Maximum number: 6]

(a)

The first three terms of an arithmetic progression are $\ln q$ , $\ln q^{4}$ and $\ln q^{7}$ , where q is a positive
constant. The sum to n terms of this progression is $4845 \ln q$ . Find the value of n.

[ 3 ]

9(a) n=57 cso 3 B1 for $\frac{n}{2}(2 \ln q+3(n-1) \ln q)$ oe soi Allow if in indices form i.e.:
$\frac{n}{2}\left(\ln q^{2}+(n-1) \ln q^{3}\right)$

B1 for $3 n^{2}-n-9690=0$ oe soi

(b)

The first three terms of a geometric progression are $p^{3 x}, p^{x}$ and $p^{-x}$ , where p is a positive
integer. Find the nth term of this progression giving your answer in the form $p^{(a+b n) x}$ .

[ 3 ]

9(b) Common ratio $=p^{-2 x}$ B1 Allow unsimplified
nth term $=p^{3 x}\left(p^{-2 x}\right)^{n-1}$ soi B1 Allow unsimplified
$p^{(5-2 n) x}$ B1

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12.4. Use finite progression formulas question 1

Question (a)

Question (b)