The third term of an A.P is 10 and the sixth term is 43 find: the first term of the sequence with shown working
The first term of an A.P can be found using the formula aₙ = a₁ + (n-1)d, where a₁ is the first term, n is the term number and d is the common difference.
In this case, a₁ = a₃ - (3-1)d
a₁ = 10 - (3-1)d
a₁ = 10 - 2d
We know that the sixth term is 43, so we can use the same formula to find the common difference.
43 = a₁ + (6-1)d
43 = 10 - 2d + 5d
43 = 10 + 3d
3d = 43 - 10
3d = 33
d = 33/3
d = 11
Substituting this value of d into the formula for a₁, we get:
a₁ = 10 - 2(11)
a₁ = 10 - 22
a₁ = -12
Therefore, the first term of the sequence is -12.