The fourth term of an ap is 37 and the sixth term is 12 more than the fourth term find the first and seventh term

Answer 1

Let's call the first term of the arithmetic progression a, and let's call the common difference d.

The fourth term of the arithmetic progression is given by a + 3d = 37.

The sixth term of the arithmetic progression is given by a + 5d = 37 + 12 = 49.

Now we have two equations with two variables:
a + 3d = 37,
a + 5d = 49.

We can solve these equations to find the values of a and d.

Subtracting the first equation from the second equation, we get:
(a + 5d) - (a + 3d) = 49 - 37,
2d = 12,
d = 6.

Substituting the value of d into the first equation, we get:
a + 3(6) = 37,
a + 18 = 37,
a = 37 - 18,
a = 19.

So the first term of the arithmetic progression is 19, and the common difference is 6.

The seventh term of the arithmetic progression is given by a + 6d = 19 + 6(6) = 19 + 36 = 55.

Therefore, the first term is 19 and the seventh term is 55.