Discussion

Explanation:

Here, 

T₁ = 1 = 1
T₂ = 3 = 1 + 2
T₃ = 3 = 1 + 2 + 3
... and so on

∴ T_n = 1 + 2 + 3 + ... + n = n(n + 1)/2 = ½ × (n² + n)

⇒ Sum of n terms =  ½ × (Σn² + Σn)

∴ Sum of first 20 terms = ½ × [(1² + 2² + 3² + ... + 20²) + (1 + 2 + 3 + ... + 20)]

= $\frac{1}{2}\left[\frac{20\times 21\times 41}{6}+\frac{20\times 21}{2}\right]$

= ½ × [2870 + 210]

= 1540

Hence, 1540.

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