NECO 2004 Mathematics · Question 16

If the first term of an AP is 1.2 and the common difference is also 2, what is the mean of the first five terms?

Options

A.2
B.4
C.5
D.8
E.10

Answer: C. 5

Explanation written with AI and checked against the answer key

The question says "first term is 1.2 and the common difference is also 2". The word "also" suggests the first term is probably 2 (the "1.2" looks like a typo), but let me check both readings. Concept For an AP, the mean of the first n terms equals the average of the first and last terms. For five terms, it equals the middle (3rd) term: a + 2d. Reading 1: a = 2, d = 2 ("also 2") Terms: 2, 4, 6, 8, 10 Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6 This gives 6, which is not among the options. Reading 2: a = 1.2, d = 2 (as printed) Terms: 1.2, 3.2, 5.2, 7.2, 9.2 Sum = 26 Mean = 26 / 5 = 5.2 This is closest to option C (5), but not exactly 5. Reading 3: a = 1, d = 2 (the "1.2" may be a garbled "1, 2") Terms: 1, 3, 5, 7, 9 Mean = 25 / 5 = 5 This matches option C exactly. Conclusion The question as printed appears to be garbled. The most sensible interpretation is a first term of 1 and a common difference of 2, which gives a mean of exactly 5. The printed version (a = 1.2) gives 5.2, which is also nearest to 5. The reading a = 2 gives 6, which is not an option, so it is probably not what was intended. Tip: For an AP with an odd number of terms, the mean is simply the middle term, a + 2d for five terms. Use it to save time. If your working doesn't match any option, check whether the question has a typo and see which reading fits the options.

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