The first, second and third terms of an arithmetic progression are $$$a, \frac{3}{2} a$$$ and $$$b$$$ respectively, where $$$a$$$ and $$$b$$$ are positive constants. The first, second and third terms of a geometric progression are $$$a, 18$$$ and $$$b+3$$$ respectively. Find the sum of the first 20 terms of the arithmetic progression. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_12 Year：2021 Question No：8(b)

Answer:

Common difference $d=6$
$
S_{20}=\frac{20}{2}(2 \times 12+19 \times 6)
$
1380

Knowledge points:

1.6.3 use the formulae for the nth term and for the sum of the first n terms to solve problems involving arithmetic or geometric progressions (Including knowledge that numbers a,b,c are 'in arithmetic progression' if 2 b=a+c (or equivalent) and are 'in geometric progression' if (or equivalent) (Questions may involve more than one progression.)

Answer:

Knowledge points:

Solution:

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