Practise applying nth-term and finite-sum formulas to arithmetic and geometric progressions, including contextual calculations, in Cambridge International Additional Mathematics.
An arithmetic progression has first term t and common difference 1.5.
The 4th, 8th and 20th terms of this arithmetic progression form the 1st, 2nd and 3rd terms of a geometric progression.
Find the value of t.
At least two correct terms from t+4.5, t+10.5, t+28.5 soi
r=t+4.5t+10.5, or r=t+10.5t+28.5, or r2=t+4.5t+28.5 oe
t+4.5t+10.5=t+10.5t+28.5 oe
Clears algebraic fractions and expands, e.g. t2+21t+110.25=t2+33t+128.25-1.5 oe nfww, and no other values
Find the common ratio of the geometric progression.
3 nfww and no other values
M1 for their (−1.5)+their 4.5their (−1.5)+their 10.5 oe, FT their t where valid.
A1