If the sum of the first two terms of a G.P. is 3, and the sum of the second and third terms is −6, find the sum of the first term and the common ratio.
Worked solution (try it first)
Write the sums in terms of a and r: a+ar=a(1+r)=3 and ar+ar2=ar(1+r)=−6.
Divide the second by the first: r=−6÷3=−2.
Then a(1−2)=3, so a=−3, and a+r=−3+(−2)=−5, option A.