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n = 1: 6*1 - 2 = 6-2 = 4
n = 2: 6*2 - 2 = 12-2 = 10
n = 3: 6*3 - 2 = 18-2 = 16
n = 4: 6*4 - 2 = 24-2 = 22
n = 5: 6*5 - 2 = 30-2 = 28
10,11,12,13,14 or 8,10,12,14,16
The sequence 4n + 7 represents a linear sequence where n is the position in the sequence. To find the first five terms, substitute n with 1, 2, 3, 4, and 5 respectively. Thus, the first five terms are 11, 15, 19, 23, and 27.
Suppose the first term is a, the second is a+r and the nth is a+(n-1)r. Then the sum of the first five = 5a + 10r = 85 and the sum of the first six = 6a + 15r = 123 Solving these simultaneous equations, a = 3 and r = 7 So the first four terms are: 3, 10, 17 and 24
x is the first term and d is the difference then x + 3d = 15 and sum of first five terms isx + (x+d) + (x+2d) + (x+3d) + (x+4d)so 5x + 10d = 55 ie x + 2d = 11As x + 3d = 15, d = 4 and x = 3,giving the five terms as 3, 7, 11, 15 and 19
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