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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 xth term of the series is
- A10 - x
- B20 - x
- C29 - x
- D30 - x
Answer not set
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CCommunity
I have read it somewhere 30 - x is correct
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CCommunity
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 Þ b = 1
From equation (i),
20 = a – 9 Þ a = 29
tx = 29 + (x –1) × –1
= 29 – x +1 = 30 – x
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 Þ b = 1
From equation (i),
20 = a – 9 Þ a = 29
tx = 29 + (x –1) × –1
= 29 – x +1 = 30 – x