General Mathematics Paper 2,Nov/Dec. 2010
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Question10

1. Given the Arithmetic Sequence -6, -2 , 1, …, 71, find the:
2. common difference;
3. number of terms of the sequence
4. The difference between the third and first terms of a Geometric Progression (G. P.) is 42. If the fourth term is greater than the second term by 168, find the:
5. first term;
6. fourth term

of the distribution.

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Observation

This question was reported to be very popular among the candidates and majority of them performed very well in it.
In part (a), candidates were able to obtain the common difference by subtracting -6 from -2  which gave 3 . They were also able to calculate the number of terms using the formula
Tn = a + (n – 1)d, where a = -6, d = 3  and obtained n = 23 i.e. the Arithmetic progression had 23 terms. However, it was also observed that some candidates used the formula
Sn = (2a + (n – 1)d) instead of Tn = a + (n – 1)d. They had wrong answers.
In part (b), candidates were expected to respond as follows:  ar2 – a = 42. i.e. a(r2 – 1) = 42. Therefore,   r2 – 1 = . Also, ar3 – ar = ar(r2 – 1) =ar( ) = 42r = 168. Therefore, r =  = 4.
r2 – 1 = 42 – 1 = 15.          a(r2 – 1) = 42 i.e. 15a = 42. Hence, the first term = a =  = 2 . The fourth term = ar3 =  x 64 = 179  or 179.2. This question was reported to have been handled satisfactorily by majority of the candidates who attempted it.