Answer
a₁ = 4
d = -3
Step-by-step explanation
a₇ = -14
S₇ = -35
using aₙ = a₁ + (n-1)d
a₇ = a₁ + (7 -1)d
a₇ = a₁ + 6d
substitute a₇ = -14, we have
-14 = a₁ + 6d
a₁ + 6d = -14 --------(i)
Sₙ = n/2[2a₁ + (n-1)d]
S₇ ⇒ n = 7
S₇ = 7/2[2a₁ + (7 - 1)d]
Substitute S₇ = -35, we have
-35 = 7/2[2a₁ + 6d]
Cross multiplying and opening the bracket yields
7(2a₁ + 6d) = -70
Divide both sides by 7
2a₁ + 6d = -70/7
2a₁ + 6d = -10 -------(ii)
Comparing equation (i) and (ii) and substract (i) from (ii)
a₁ + 6d = -14 --------(i)
2a₁ + 6d = -10 -------(ii)
2a₁ - a₁ = -10 - (-14)
a₁ = -10 + 14
a₁ = 4
To find d, substitute a₁ = 4 into equation (i)
Recall (i) a₁ + 6d = -14
4 + 6d = -14
6d = -14 - 4
6d = -18
d = -18/6
d = -3