Explanation:
arithmetic sequence :
a1 = 7
d = 3
an = an-1 + d = a1 + (n-1)×d
the formula for the sum of an arithmetic sequence is
n/2 × (2×a1 + (n-1)×d)
40 is a12 (n = 12), as 40-7 = 33, 33/3 = 11, 11 plus 1 from a1 is 12.
we have the sum of 12 terms.
12/2 × (2×7 + 11×3) = 6 × (14 + 33) = 6×47 = 282
so, we have :
the sum = 282
A = 12
B = 7 + (n-1)×3 = 7 + 3n - 3 = 4 + 3n