Find the next three terms in the sequence
3, 12, 21, 30, . . .
looks to me as the sequence is to add 9 to the last number...
12 - 3 = 9
21 - 12 = 9
31 - 21 = 9
The common difference of successive members is 9
This is arithmetic progression.
In arithmetic progression:
an = a1 + ( n - 1 ) * d
In this case:
a1 = 3 , d = 9
an = a1 + ( n - 1 ) * d
an = 3 + ( n - 1 ) * 9
an = 3 + 9 n - 9
an = 9 n - 6
n = 1
a1 = 9 * 1 - 6 = 9 - 6 = 3
n = 2
a2 = 9 * 2 - 6 = 18 - 6 = 12
n = 3
a3 = 9 * 3 - 6 = 27 - 6 = 21
n = 4
a4 = 9 * 4 - 6 = 36 - 6 = 30
n = 5
a5 = 9 * 5 - 6 = 35 - 6 = 39
n = 6
a1 = 9 * 6 - 6 = 56 - 6 = 48
n = 7
a1 = 9 * 7 - 6 = 63 - 6 = 57
The next three terms:
39 , 48 , 57
Does anyone have all the answers
3,12,21,30,...if an = 201
Hmmm, let me think... Oh, I see what's happening here! It looks like the pattern is just adding 9 to each term. So, if we follow this pattern, the next three terms would be 39, 48, and 57. Voila!
To find the next terms in the sequence, it is helpful to recognize the pattern or rule governing the sequence. In this case, we can observe that the terms in the sequence are increasing by 9 each time.
To determine the next term, add 9 to the last term in the sequence:
30 + 9 = 39
So, the next term in the sequence is 39.
To find the following terms, again add 9 to the last term in the sequence:
39 + 9 = 48
48 + 9 = 57
Therefore, the next three terms in the sequence are 39, 48, and 57.