The sum of the first nine terms of an arithmetic progression is 117 . The sum of the next four terms is 91. Find the first term and the common difference of the progression. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_s20_qp_11 Year：2020 Question No：1
Answer:
\[
117=\frac{9}{2}(2 a+8 d)
\]
Either \(91=S_{4}\) with ' \(a\) ' as \(a+4 d\) or \(117+91=S_{13}\) (M1 for overall approach. M1 for \(S_{n}\) )
Simultaneous Equations \(\rightarrow a=7, d=1.5\)
117=\frac{9}{2}(2 a+8 d)
\]
Either \(91=S_{4}\) with ' \(a\) ' as \(a+4 d\) or \(117+91=S_{13}\) (M1 for overall approach. M1 for \(S_{n}\) )
Simultaneous Equations \(\rightarrow a=7, d=1.5\)
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.)
Solution:
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