# series

2(a)Consider the arithmetic progression with terms A3=-2 and A12=23. Find the sum of A1+......+A40 (can do)
(b)In 1800 the population of England was 8 million. The economist Malthus (1766-1834) produced a hypothesis, suggesting:-that the population of england would increase, according to a G.P., by 2% per year
-that the english agriculture production,able to feed 10 million people in 1800,would improve according to an A.P. to feed an extra 400000 people every year

Po represents the english population in 1800 and Pn that population in the year 1800+n:
(i)express,according to Malthus' hypothesis Pn as a function n.

Ao represents the number of people that the english agriculture production can feed in 1800 and An that number in 1800+n:
(ii)express,according to Malthus' hypothesis,An as a function of n
(iii)Calculate the population of england in 1900 and the number of people that the english agriculture production can feed in 1900
(iv)Determine the year from which the english agriculture can no longer feed the english population according to Malthus' hypothesis(-use your calculator by graphing or creating the lists:n=L1;Pn=L2;An=L3 tp compare increases

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1. b i)
a = 8 000 000
r = 1.2
Pn = 8 000 000 x 1.2^(n-1)

b ii)
a = 8 000 000
d = 400 000
Pn = 8 000 000 + (n-1)400 000
= 7 600 000 + 400 000n

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