How to find an arithmetic progression if its 6 and 8 terms are -4.6 and -4.2, respectively?

1. For the n-th member of the arithmetic progression an we have the formula:

an = a1 + (n – 1) d, where:
a1 – first term;
d – the difference of the progression.
2. For the 6th and 8th members, we get:

a6 = a1 + (6 – 1) d = a1 + 5d; (1)
a8 = a1 + (8 – 1) d = a1 + 7d. (2)
Subtracting the first from the second equation, we get:

a8 – a6 = (a1 + 7d) – (a1 + 5d) = 2d, hence:
d = (a8 – a6) / 2.
3. Substitute the given values:

a6 = -4.6;
a8 = -4.2;
d = (-4.2 – (-4.6)) / 2 = (-4.2 + 4.6) / 2 = 0.4 / 2 = 0.2.
4. First term:

a1 = a6 – 5d = -4.6 – 5 * 0.2 = -4.6 – 1 = -5.6.

Answer: a1 = -5.6; d = 0.2.