# Maths

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1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is 4/3 less than the sum of the first 3 terms of the geometric progression.Determine the value of r,the common ratio of the geometric progression

2..a new sequence is formed by adding together the corresponding terms of a geometric sequence and an arithmetic sequence.The common ratio of the geometric sequence is 2 and the common difference of the arithmetic sequence is 2.The first term of the new sequence is 1,and the second term is 7...
2.1 calculate the third term of the new sequence
2.2write down an expression for the n-th term of the new sequence

• Maths - ,

a+d = ar
a = 12
r < 1
3/2 (2a+2d) = a(1+r+r^2) - 4/3

3ar = a(1+r+r^2) - 4/3
36r = 12(1+r+r^2) - 4/3
r = 2/3 or 4/3

r=2/3:
12+d = 12* 2/3
d = -4

AP = 12 8 4 0 ...
GP = 12 8 16/3 32/9 ...

check
12+8+4 = 12+8+16/3 - 4/3 YES

• Maths - ,

4/3

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