In a series of numbers , the next number is formed by adding 2 to the sum of…
2024
In a series of numbers , the next number is formed by adding 2 to the sum of the previous number , and the 9th number is 896 . Then what is the first number in the series ?
- A.
8
- B.
7
- C.
6
- D.
5
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Correct answer: D
Answer: 5
Let the first term be x. The second term is x + 2. From the third term onward each term is twice the previous term, so for n ≥ 2 the nth term is 2^(n-2) × (x + 2).
For n = 9: T9 = 2^7 × (x + 2) = 128 × (x + 2).
Set 128 × (x + 2) = 896, so x + 2 = 896 / 128 = 7, hence x = 5.
Check: second term = 7, then doubling repeatedly gives T9 = 896, so the first term 5 is correct.