Find the first term and the common difference of the arithmetic sequence if a2-a6+a4=-7 and a8-a7=2a4

We'll write both given relation from enunciation with
respect to the first term and the common
difference:

a2-a6+a4 = (a1 + d) - (a1 + 5d) + (a1 +
3d)

We'll eliminate and combine like terms and we'll
get:

a1 - d = -7

The first
equation has been changed into a1 - d = -7.

We'll write the
2nd relation from enunciation with respect to the first term and the common
difference:

a8-a7 = (a1 + 7d) - (a1 +
6d)

We'll eliminate and combine like terms and we'll
get:

d = 2a4

d = 2(a1 +
3d)

d = 2a1 + 6d

2a1 + 5d =
0

a1 = -5d/2

-5d/2  - d =
-7

-5d - 2d = -14

-7d =
-14

d = 2

a1 =
-5*2/2

a1 =
-5

The first term and the common difference
of the arithmetical sequence are: a1 = -5 and d =
2.