This is a GP with a = 5 , r = 15/5 = 3, n = 7
S_n = a(rⁿ - 1 )/(r - 1)

Correct Option: C

This is a GP with a = 5 , r = 15/5 = 3, n = 7
S_n = a(rⁿ - 1 )/(r - 1)
⇒ S₁₅ = 5(3⁷ - 1)/(3 - 1)
= 5/2(3⁷ - 1)
= 5/2 (2187 - 1)
= ₹ 5465

In the given AP,
we have a = 13 , d = (8 - 13) = -5 and n = 10
T_n = a + (n - 1)d

Correct Option: A

In the given AP,
we have a = 13 , d = (8 - 13) = -5 and n = 10
T_n = a + (n - 1)d
T₁₀ = 13 + (10 - 1) - 5
= 13 + 9 x (-5) = 13 - 45 = -32

We have, a = 10 , d = (8 - 10) = -2, T_n = - 28
T_n = a + (n - 1)d

Correct Option: D

We have, a = 10 , d = (8 - 10) = -2, T_n = - 28
T_n = a + (n - 1)d
⇒ -28 = 10 + (n - 1) x (- 2)
⇒ -28 = 10 - 2n + 2
⇒ 2n = 12 + 28
⇒ 2n = 40
∴ n = 20

T₉ = a + (9 - 1)d = a + 8d
T₅ = a + (5 - 1)d = a + 4d
T₉ - T₅ = 32
⇒ (a + 8d) - (a + 4d) = 32
⇒ 4d = 32
∴ d = 8
T₉ + T₅ = (a + 8d) + (a + 4d)
= 2a + 12d
T₉ + T₅ = 114

Correct Option: C

T₉ = a + (9 - 1)d = a + 8d
T₅ = a + (5 - 1)d = a + 4d
T₉ - T₅ = 32
⇒ (a + 8d) - (a + 4d) = 32
⇒ 4d = 32
∴ d = 8
T₉ + T₅ = (a + 8d) + (a + 4d)
= 2a + 12d
T₉ + T₅ = 114
⇒ 114 = 2(a + 6d)
⇒ a + 6d = 57
∴ T₈ = a + 7d
= a + 6d + d
= 57 + 8 = 65

This is an AP with a = 1 and d = 7
∴ 11th term = a + (n - 1) x d = 1 + (11 - 1) x 7

Correct Option: C

This is an AP with a = 1 and d = 7
∴ 11th term = a + (n - 1) x d = 1 + (11 - 1) x 7
= 1 + 10 x 7 = 71