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Answer (4)
a 1 = 2 a 2 = 4 ∗ a 1 − 1 = 4 ∗ 2 − 1 = 7 a 3 = 4 ∗ a 2 − 2 = 4 ∗ 7 − 2 = 26 a 4 = 4 ∗ a 3 − 3 = 4 ∗ 26 − 3 = 101 a 5 = 4 ∗ a 4 − 4 = 4 ∗ 101 − 4 = 400 a 6 = 4 ∗ a 5 − 5 = 4 ∗ 400 − 5 = 1595
The next** number **in the sequence is 1595.
Here, given that, the sequence of numbers is: 2,7,26,101,400....
The** relationship** between the successive numbers in the sequence:
x ( n + 1 ) = 4 x n − n
Now, applying it to the given sequence:
x 1 = 2 x 2 = 4 ∗ 2 − 1 = 7 x 3 = 4 ∗ 7 − 2 = 26 x 4 = 4 ∗ 26 − 3 = 101 x 5 = 4 ∗ 101 − 4 = 400
As we can see, the formula x ( n + 1 ) = 4 x n − n holds true for each term in the sequence, and it gives us the correct values for the subsequent terms.
Now, to find the next number in the** sequence**,
we use the formula with n = 5:
x ( 5 + 1 ) = 4 ∗ x 5 − 5 x 6 = 4 ∗ 400 − 5 x 6 = 1600 − 5 x 6 = 1595
So, the next number in the sequence is 1595.
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The next number in the sequence 2, 7, 26, 101, 400 is 1595. This is derived from the recurrence relation x ( n + 1 ) = 4 x n − n applied to the previous terms. Using this formula, we find that the computation for the sixth term yields 1595.
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