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For the sequence 1, 7, 25, 79, 241, 727 … simple formula for {an} is ____________ 
  • a)
    3n+1 – 2 
  • b)
    (-3)n + 4
  • c)
    n2 – 2
  • d)
    3n – 2 
Correct answer is option 'D'. Can you explain this answer?
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For the sequence 1, 7, 25, 79, 241, 727 … simple formula for {a...
The ratio of consecutive numbers is close to 3. Comparing these terms with the sequence of {3n} which is 3, 9, 27 …. Comparing these terms with the corresponding terms of sequence {3n} and the nth term is 2 less than the corresponding power of 3.
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For the sequence 1, 7, 25, 79, 241, 727 … simple formula for {a...
To find the pattern in this sequence, let's look at the differences between consecutive terms:

7 - 1 = 6
25 - 7 = 18
79 - 25 = 54
241 - 79 = 162
727 - 241 = 486

The differences between consecutive terms are increasing by a factor of 3 each time. So, we can say that the nth term is given by:

T(n) = T(n-1) + 3^(n-1)

Using this formula, we can find the value of the 7th term:

T(7) = T(6) + 3^(7-1)
= 727 + 3^6
= 727 + 729
= 1456

Therefore, the 7th term in the sequence is 1456.
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