In an arithmetic progression, c7 = -6 c11 = -12 are known. find c1 and d.

In an arithmetic progression, the n – term can be calculated by the formula

c (n) = c (1) + (n – 1) d, where

c (1) is the first member of this progression;

n is the number of the calculated member;

d – the difference of the arithmetic progression.

If c (7) = -6 and c (11) = -12 are known, then

-6 = c (1) + (7 – 1) d;

-12 = c (1) + (11 – 1) d

obtained a system of 2 equations with 2 unknowns.

Subtract the second from the first equation:

6 = -4 d,

where

d = -1.5.

Substitute d in the first equation, then

-6 = c (1) + 6 * (-1.5) and

c (1) = 3.

Answer: c (1) = 3 and d = -1.5.