Question

Find value of a = 0 and d for A.P. 3, 6, 9, 12​

Answer 1

Answer:

Notice the difference between each term of the sequence is 3. From there, you can build up your reasoning.

First term is 3.

Second term is 3 + 3 = 6

Third term is 3 + 3 + 3 = 9

Fourth term is 3 + 3 + 3 + 3 = 12

Do you notice any pattern? You might notice the pattern if the terms are written like this:

First term is 3. Three is 3 x 1

Second term is 6. Six is 3 x 2

Third term is 9. Nine is 3 x 3

Fourth term is 12. Twelve is 3 x 4

Looking at the sequence that way hopefully give you an intuition about how the nth term should look like. For example, without continuing the list, I know that the 10th term of the sequence should be 3 x 10 = 30. Therefore, the nth term of the sequence should be 3 x n = 3n.

But the sequence can also be written like this:

First term is 3 + 0 x 3

Second term is 3 + 1 x 3

Third term is 3 + 2 x 3

Fourth term is 3 + 3 x 3

By looking at the sequence from this perspective, one can formulate a new rule for the nth term of that sequence like this: 3+(n−1)∗3=3+3n−3=3n

This way of looking the sequence might seem more complicated than the previous one. But it has its advantage because it is more general. It can be applied to various sequences as long as the difference is constant.

Suppose we encounter a different sequence: 3, 7, 11, 15. This sequence’s pattern might not seem as ‘obvious’ like your question. But if we write the sequence this way:

First term is 3 + 0 x 4

Second term is 3 + 1 x 4

Third term is 3 + 2 x 4

Fourth term is 3 + 3 x 4

we can tell the sequence rule for nth term is 3+(n−1)∗4=3+4n−4=4n−1

Can you intuitively see that the sequence 3, 7 , 11, 15 is equal to (4–1), (8–1), (12–1), and (16–1) respectively? I don’t think so, at least not for me.

This particular sequence with constant difference has a name. It’s called arithmetic sequence. If the first term is called a and the constant difference is called b , then the formula for finding the nth term of the sequence is a+(n−1)∗b

Answer 2

Answer:

a=3and d=3

Step-by-step explanation:

a is the first term of the arithmetic progression and in this given data a=3

d is the common difference between the terms like term -2 -- term-1 (or) term(3)-term(4) like that

here in given data d =6-3=3

so a=3 and d=3