Write the first 5 terms of the sequences defined by the recursive formula

t1= 7, tn= 2tn-1 - 3n, n>1

just plug in the values for n:

t1 = 7
t2 = 2t1-3(2) = 2(7)-3(2) = 8
t3 = 2(8)-3(3) = 7
...

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To find the first 5 terms of the sequence defined by the recursive formula, we start with t1 = 7 and use the formula tn = 2tn-1 - 3n for n > 1.

Using this information, we can find the values of t2, t3, t4, and t5.

1. t1 = 7 (given)
2. t2 = 2t1 - 3(2) = 2(7) - 3(2) = 14 - 6 = 8
3. t3 = 2t2 - 3(3) = 2(8) - 3(3) = 16 - 9 = 7
4. t4 = 2t3 - 3(4) = 2(7) - 3(4) = 14 - 12 = 2
5. t5 = 2t4 - 3(5) = 2(2) - 3(5) = 4 - 15 = -11

Therefore, the first 5 terms of the sequence are:
t1 = 7
t2 = 8
t3 = 7
t4 = 2
t5 = -11

To find the first five terms of the sequence defined by the recursive formula t1= 7 and tn = 2tn-1 - 3n for n > 1, we can apply the formula multiple times.

Let's go step by step:

t1 = 7 (given in the formula)
t2 = 2t1 - 3(2) = 2(7) - 6 = 14 - 6 = 8
t3 = 2t2 - 3(3) = 2(8) - 9 = 16 - 9 = 7
t4 = 2t3 - 3(4) = 2(7) - 12 = 14 - 12 = 2
t5 = 2t4 - 3(5) = 2(2) - 15 = 4 - 15 = -11

Therefore, the first five terms of the sequence are 7, 8, 7, 2, -11.