For a given A.P. with

T₁₀ = 41, S10 = 320, find T_n, S_n.

Formula used.

S_n = [a + a_n]

T_n = a_n = a + (n–1)d

S_n = [2a + (n–1)d]

⇒ S₁₀ = 320

⇒ T₁₀ = a₁₀ = 41

S₁₀ = [a + 41]

320 = [a + 41]

= a + 41

64 = a + 41

a = 64–41

⇒ a = 23

a₁₀ = a + (n–1)d

41 = 23 + (10–1)d

41–23 = 9d

9d = 18

⇒ d = = 2

T_n = a_n = a + (n–1)d

T_n = 23 + (n–1)2

23–2 + 2n

21 + 2n

S_n = [2a + (n–1)d]

S_n = [2×23 + (n–1)2]

= [46 + 2n–2]

= [44 + 2n]

= n[22 + n]

= 22n + n²