Write a recursive formula for the sequence of numbers.

Step-by-step explanation:

an = a1 + 4×[2^(n -1) - 1]

9514 1404 393

  a[1] = 3

  a[n] = 2×a[n-1] +1

Step-by-step explanation:

We observe the first differences are ...

  7-3 = 4

  15-7 = 8

  31-15 = 16

  63-31 = 32

The first differences increase by a factor of 2, so we expect the recursive formula will have a term that looks like "2×a[n-1]".

The second term is 2·3+1 = 7.

The third term is 2·7+1 = 15.

This suggests our recursive formula is ...

  a[1] = 3

  a[n] = 2×a[n-1] +1

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x

step-by-step explanation:

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