tn - tn-1 = 2n + 3
Find the first five terms in the sequence using this recursive formuls
You'll need T1 (first term) to find the remaining terms.
To find the first five terms in the sequence using the given recursive formula tn - tn-1 = 2n + 3, we need to start with an initial term and then use the formula to generate the subsequent terms.
Let's begin by determining the initial term, t1. With the recursive formula, we do not have t0 given, so we'll need to choose a value to start the sequence.
For simplicity, let's consider t1 = 0.
Now, we can apply the recursive formula to find the subsequent terms.
Term 1: t1 = 0
Since this is our initial term, we don't need to use the formula. We already have t1 = 0.
Term 2: t2 = t1 + (2*1 + 3) = 0 + 2 + 3 = 5
Term 3: t3 = t2 + (2*2 + 3) = 5 + 4 + 3 = 12
Term 4: t4 = t3 + (2*3 + 3) = 12 + 6 + 3 = 21
Term 5: t5 = t4 + (2*4 + 3) = 21 + 8 + 3 = 32
Therefore, the first five terms in the sequence using the given recursive formula tn - tn-1 = 2n + 3 are: 0, 5, 12, 21, 32.