If the 10th term of the sequence a, a

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If the 10th term of the sequence a, a – b, a –2b, a – 3b, ... is 20 and the 20th term is 10, then the x th term of the series is

1. 10 – x
2. 20 – x
3. 29 – x
4. 30 – x

Correct Option: D

Suppose a, a – b, a –2b ..... is an AP with first term = a and common difference = – b
Now, t₁₀ = a + (10 – 1) × (–b)
⇒ 20 = a – 9b .... (i)
t₂₀ = a + (20 – 1) × (–b)
⇒ 10 = a – 19 b ... (ii)
From equation (i) – (ii),
20 – 10 = a – 9b – a + 19 b
⇒ 10b = 10
⇒ b = 1
From equation (i) ,
20 = a – 9 ⇒ a = 29
∴ t_x = 29 + (x – 1) × (–1 )
t_x = 29 – x + 1 = 30 – x