Lavza asked in Science & MathematicsMathematics · 6 months ago

# A sequence is formed from an inductive relationship: Un+1=2Un+5. given that U1=2, find the first four terms of the sequence.?

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• 6 months ago

A sequence is formed from an inductive relationship: U n + 1 = 2 U n + 5.

Given that U 1 = 2, the first four terms of the sequence:

2, 9, 23, 51

• JOHN
Lv 7
6 months ago

Un+1 = 2Un +5 means double the previous number and add 5.

Starting with 2: 2 x 2 +5 = 9

Next: 2 x 9 + 5 = 23

Next 2 x 23 + 5 = 51

The 1st four terms are 2, 9, 23, 51.

• 6 months ago

This is one of those cases where we need a clear notation for subscripts to make sense of that equation.

I will use the format

X[k]

to indicate k is a subscript of X.

In this notation, I believe the equation for the relationship is meant to be

U[n+1] = 2 U[n] + 5

(That is, the +1 is inside a subscript and the +5 is not.)

So we would have

U[1] = 2

U[2] = 2 U[1] + 5 = 4 + 5 = 9

U[3] = 2 U[2] + 5 = 18 + 5 = 23

U[4] = 2 U[3] + 5 = 46 + 5 = 51