-  The 10th term is 31
31 = a + (10 - 1) d
46 = a + (15 - 1) d
Solving these equations  a=4 and d=3
Series 4, 7, 10

To find the correct answer, we can use the formula for the nth term of an arithmetic progression (A.P):

an = a1 + (n-1)d

where

an is the nth term of the A.P

a1 is the first term of the A.P

d is the common difference between the terms of the A.P

n is the number of terms in the A.P

Let's use this formula to solve the problem:

Given, a10 = 31 and a15 = 46

Using the formula for the nth term of an A.P, we have:

a10 = a1 + 9d = 31 ----(1)

a15 = a1 + 14d = 46 ----(2)

Subtracting equation (1) from (2), we get:

5d = 15

d = 3

Now, substituting the value of d in equation (1), we get:

a1 + 9(3) = 31

a1 = 4

Therefore, the first term of the A.P is 4 and the common difference is 3.

Using the formula for the nth term of an A.P, we can find the series:

a1 = 4

d = 3

an = a1 + (n-1)d

Using this formula, we get the following series for n = 1 to 3:

a1 = 4

a2 = a1 + d = 7

a3 = a1 + 2d = 10

Therefore, the series is 4, 7, 10, which corresponds to Option A.

In conclusion, the correct answer is Option A, and the series is 4, 7, 10.