In a sequence of numbers, each term except the first is 4 less than 4 times the previous term. If the fourth term in this sequence is 12, what is the first term?

First term is -1 because the common difference between each term 4n-4 where n is the term before. Therefore of you work backwards by taking 4 away from 12 then diving by 4 you should get 4 as third term. So you can keep going back till first term and you would get the following sequence
-1, 0, 4, 12...

Answered by krish26 | 2024-06-10

The problem states that each term in a sequence is 4 less than 4 times the previous term, and we know the fourth term is 12. To find the first term, we need to work backwards from the fourth term. The formula for a term in the sequence, given a previous term, is next term = 4(previous term) - 4. Restating the fourth term as the 'next term' in the series that stems from the third term, and applying this formula backwards, we can deduce the value of previous terms.
Let's label the terms of the sequence as T1 (first term), T2 (second term), T3 (third term), and T4 (fourth term) = 12. Starting with T4, we have:

T3 = (T4 + 4) / 4
T2 = (T3 + 4) / 4
T1 = (T2 + 4) / 4

By substituting T4 = 12 into the equations:

T3 = (12 + 4) / 4 = 4
T2 = (4 + 4) / 4 = 2
T1 = (2 + 4) / 4 = 1.5

Therefore, the first term in this sequence is 1.5.

Answered by qwarrow | 2024-06-24

To find the first term of the sequence, we applied the formula relating each term to the previous one. Working backwards from the given fourth term, we calculated each preceding term until we reached the first term. The first term is 1.5 .
;

Answered by krish26 | 2024-10-12