Question

In an arithmetic progression if an

= 3n-2, then find the second term of the progression​

Answer 1

Answer:

You don’t need to know whether it is an A.P., since you provide the formula. Therefore, for n = 10 it follows t(10) = 3*10 - 2 = 28.

Now to the first question:

If it is an Arithmetic Progression, then between any consecutive terms there is a constant ‘Common Difference’.

Let t(k) be the k-th term. By definition, t(k) = 3k - 2 and t(k+1) = 3(k + 1) - 2.

Taking the difference, Δt = t(k+1) - t(k) = [3(k + 1) - 2] - (3k - 2) = 3

So, the difference between terms is a constant not dependent on the value of k and the sequence is an Arithmetic one.

Answer 2

The second term of an A.P is 4.

A.P (Arithmetic Progression)

Arithmetic progression is a progression in which each phrase after the first is derived by adding a constant value known as the common difference to the previous term (d).

Formula:

We know a = a1 + (n – 1)d to get the nth term of an arithmetic progression. The first term is a1, the second is a1 + d, the third is a1 + 2d, and so on.

Given:

an =  3n-2,

Explanation:

To evaluate the terms of A.P,

Put the value of n = 1,2,34,....

For, the first term of an A.P put n = 1,

a1 = 3×1 - 2

a1 = 1

For, the second term of the A.P put n = 2,

a2 = 3×2 - 2

a2 = 4

Thus, the second term of an A.P is 4.

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