Question

Another sequence is defined by a term to term sequence where k and r are constants

Answer 1

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$U(n + 1) = kU(n) + r$

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$n = 1$

$U(1 + 1) = kU(1) + r$

$U(2) = k \times U(1) + r$

$188 = k \times (37) + r$

$37k + r = 188 \: \: \: (( \alpha ))$_________________________________

$n = 2$

$U(2 + 1) = kU(2) + r$

$U(3) = k \times U(2) + r$

$943 = k \times (188) + r$

$188k + r = 943 \: \: \: (( \beta ))$

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$188k + r = 943 \: \: \: (( \beta ))$

$37k + r = 188 \: \: \: \: \: (( \alpha ))$

$(( \beta )) - (( \alpha )) =$

$188k - 37k + r - r = 943 - 188$

$151k = 755$

Divide sides by 151

$\frac{151k}{151} = \frac{755}{151}$

$k = 5$

Put the value of k in one of the equations to find the r :

$37k + r = 188$

$37 \times (5) + r = 188$

$185 + r = 188$

$r + 185 = 188$

Subtract sides 185

$r + 185 - 185 = 188 - 185$

$r = 3$

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