C1 2016 6 Edexcel

6

a) Using a_1=4 we obtain a_2=5-4k, a_3=5-k(5-4k)=5-5k+20k^2.

b)The required sum is equal to 1+a_1+1+a_2+1+a_3=1+4+1+5-4k+1+5-5k+20k^2=17-9k+20k^2.

c) By the conditions:
a_{r+1}+k×a_r=5-k×a_r+k×a_r=5 .

Now each term in the sum is equal to 5 then the sum is equal to 100×5=500.

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