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If the first three terms of the arithmetic sequence an are A-1, a + 1 and 2a-3 respectively, then the general term formula of this sequence is?
The difference between A-1 and a + 1 is 2, indicating that the tolerance is 2
So:
2a-3 - (a+1) = 2
a-4 =2
a =6
Therefore, the first item is 5, the second item is 7, and the third item is 9
The general formula is: an = 5 + 2 (n-1)
= 3 + 2n
Given that the first three terms of the arithmetic sequence {an} are A-1, 2A + 1 and a + 7 respectively, the general term formula of this sequence is______ ．
The first three terms of ∵ arithmetic sequence {an} are A-1, 2A + 1, a + 7, and ∵ 2 (2a + 1) = A-1 + A + 7. The solution is a = 2. A1 = 2-1 = 1, A2 = 2 × 2 + 1 = 5, A3 = 2 + 7 = 9. The ∵ sequence an is a arithmetic sequence with 1 as the first term and 4 as the period, and ∵ an = 1 + (n-1) × 4 = 4n-3
If LG2, LG (2x-1), LG (2x + 3) are in arithmetic sequence, then the value of X is equal to______ ．
∵ LG2, LG (2x-1), LG (2x + 3) are in arithmetic sequence, ∵ 2lg (2x-1) = LG2 + LG (2x + 3), ∵ LG (2x-1) 2 = LG (2x + 1 + 6), which is reduced to (2x-1) 2 = 2x + 1 + 6 and sorted into (2x) 2-4 × 2x-5 = 0, that is, (2x-5) (2x + 1) = 0, (*) ∵ 2x > 0, ∵ 2x + 1 > 1, ∵ (*)
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