Given the third term of an arithmetic sequence less than the fourth term by three. The seventh term is two times the fifth term. Find the common difference and the first term.

The first term is -6 and common difference is 3

Step-by-step explanation:

The nth term of an arithmetic progression is expressed as;

Tn = a + (n-1)d

T3 = a+2d

T4 = a + 3d

If the third term of an arithmetic sequence less than the fourth term by three

T3 = T4 - 3

a+2d = a+3d - 3

2d - 3d = -3

-d  = -3

d = 3

Similarly;

T7 = a+6d

T5 = a+4d

If the seventh term  is two times the fifth term, the;

T7 = 2T5

a+6d = 2(a+4d)

a+6d = 2a+8d

Since d = 3

a + 6(3) = 2a + 8(3)

a+18 = 2a + 24

a-2a = 24 - 18

-a = 6

a = -6

Hence the first term is -6 and common difference is 3

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.