If Sn n3 n2 n 1 where Sn denotes the sum of the first n terms of a series and tm 291 then m is equal...........

Quantitative Aptitude ( CCS) Arithmetic progression

If S_n = n³ + n² + n + 1 , where S_n denotes the sum of the first n terms of a series and t_m = 291, then m is equal to?

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Explanation:

S_n - S_n = t_n
Substitute m instead of n
S_m - S_m-1 = t_m
We know that S_n = n³ + n² + n + 1
Hence m³ + m² + m + 1
m³ + m² + m + 1 - [(m-1)³ + (m-1)² + (m-1) + 1 ] = 291
m³ + m² + m + 1 - [m³ - (3m)² + 3m - 1 + m² - 2m + 1 + m - 1 + 1] = 291
1 + (3m)² + 3m + 1 -2m - 1 = 291
(-3m)² + m - 290 = 0
(3m)² - m + 290 = 0
Solving above equation we get m = -29, 30
M cannot be negative
Hence m = 30