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a = 8
d = 1/3
Sn = 168
=> n/2 [ 2a +(n - 1)d] = 168
=> n [ 16 + (n-1) / 3] = 168 * 2
=> n( 48 +n-1) / 3 = 336
=> n( 47 + n) = 1008
=> n^2 + 47n = 1008
=> n^2 +47n - 1008 = 0
=> n^2 + 63n - 16n - 1008 = 0
=> n(n+63) - 16(n+63) = 0
=> (n+63)(n-16) = 0
n= 16 and - 64
No. Of students can't be negative,
So,
Total number of students = 16
d = 1/3
Sn = 168
=> n/2 [ 2a +(n - 1)d] = 168
=> n [ 16 + (n-1) / 3] = 168 * 2
=> n( 48 +n-1) / 3 = 336
=> n( 47 + n) = 1008
=> n^2 + 47n = 1008
=> n^2 +47n - 1008 = 0
=> n^2 + 63n - 16n - 1008 = 0
=> n(n+63) - 16(n+63) = 0
=> (n+63)(n-16) = 0
n= 16 and - 64
No. Of students can't be negative,
So,
Total number of students = 16
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