If the sum of the first 14 terms of an AP is 1050 and its first term is 10

• Arithmetic Progression (C10)

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

Solution

Here,

S₁₄ = 1050

n = 14,

a = 10

S_n = n/2 [2a + (n - 1)d]

1050 = 14/2 [20 + 13d]

1050 = 140 + 91d

910 = 91d

d = 10

Therefore,

a₂₀ = 10 + (20 – 1) × 10 = 200

The 20th term is 200.