Solve for n:
(2 n + 1)/3 = 43/3
Multiply both sides of (2 n + 1)/3 = 43/3 by 3:
1 (2 n + 1) = 3×43/3
3×43/3 = (3×43)/3:
(3 (2 n + 1))/3 = (3×43)/3
(3 (2 n + 1))/3 = 3/3×(2 n + 1) = 2 n + 1:
2 n + 1 = (3×43)/3
(3×43)/3 = 3/3×43 = 43:
2 n + 1 = 43
n = 21
To clarify the above answer, consider this:
Sum of squares of consecutive numbers =1/6[2n +1) * n * (n +1)..........(1)
Sum of consecutive numbers =1/2[n * (n +1)].......................(2)
Divide (1) by (2) and you get: = 1 /3 *(2n +1)
1/3[2n +1] =43/3 Cross multiply
2n +1 = 43
Therefore: n = 21
