The first term in a sequence of number is t1 = 4. The terms that follow are defined by the formula: tn - tn-1 = 3n -2. Determine the value of t50.
so
t2 = t(1) + 3(2) - 2 = 4 + 4 = 8
t3 = t2 + 3(3)-2 = 8 + 7 = 15
t4 = t3 + 3(4) - 2 = 15+10=25
t5 = t4 + 3(5) - 2 = 25+13 = 38
so the sequence is
4 8 15 25 38 ...
first differences: 4 7 10 13 ....
second diff : 3 3 3 3 ...
ahhh, so the expression is quadratic.
see if can come up with a quadratic to express the sequence 4 8 15 25 38 ....
To determine the value of t50, we need to find the pattern of the sequence and then apply the given formula to calculate each term one by one until we reach t50.
Given the formula tn - tn-1 = 3n -2, we can start by calculating the second term, t2.
The formula tells us that t2 - t1 = 3(2) - 2. Since t1 = 4, we have t2 - 4 = 6 - 2, which simplifies to t2 - 4 = 4. Therefore, t2 = 4 + 4 = 8.
Now we can continue this process and calculate the third term, t3. Using the same formula, we have t3 - t2 = 3(3) - 2. Since t2 = 8, we have t3 - 8 = 9 - 2, which simplifies to t3 - 8 = 7. Therefore, t3 = 7 + 8 = 15.
We can continue this process for the next terms until we reach t50. Here's a table showing the calculation step by step:
n tn tn - tn-1
------------------------------
1 4 -
2 8 4
3 15 7
4 25 10
5 38 13
6 54 16
... ... ...
49 240 143
50 ? ?
As we progress, notice that the differences between tn values (tn - tn-1) increase by 3 with each term. Therefore, we can deduce that the difference for t50 will be 3 * (50 - 1), which is 3 * 49 = 147.
Now, to find t50, we can add this difference to the last calculated term, t49. Thus, t50 = t49 + 147.
From the table above, we know that t49 = 240. Therefore, t50 = 240 + 147 = 387.
So, the value of t50 is 387.