(d)* $$ 3 x-7,2 x $$ and $$ 3 x+1 $$ are the fifth, sixth and seventh terms of a linear number patern. (1) Determine the value of $$ x $$ and hence determine the constant difference. (2) Determine the general term of the number pattern. (3) Which term in the pattern is the first to be greater than 200 ? (e)* Consider the linear number pattern $$ 6 ; 6+x ; 6+2 x ; 6+3 x ; \ldots $$ (1) Write down the fifth term of the number pattern in terms of $$ x $$. (2) Determine the $$ 100^{ ext {th }} $$ term of the number pattern in terms of $$ x $$. (3) If the $$ 100^{ ext {th }} $$ term is 303 , determine the value of $$ x $$.

Question

(d)* $$ 3 x-7,2 x $$ and $$ 3 x+1 $$ are the fifth, sixth and seventh terms of a linear number patern. (1) Determine the value of $$ x $$ and hence determine the constant difference. (2) Determine the general term of the number pattern. (3) Which term in the pattern is the first to be greater than 200 ? (e)* Consider the linear number pattern $$ 6 ; 6+x ; 6+2 x ; 6+3 x ; \ldots $$ (1) Write down the fifth term of the number pattern in terms of $$ x $$. (2) Determine the $$ 100^{	ext {th }} $$ term of the number pattern in terms of $$ x $$. (3) If the $$ 100^{	ext {th }} $$ term is 303 , determine the value of $$ x $$.

UpStudy AI · Accepted Answer

For part (d): - $$ x = 3 $$ - Constant difference $$ d = 4 $$ - General term $$ T_n = 4n - 2 $$ - First term greater than 200 is $$ n = 51 $$. For part (e): - Fifth term: $$ 6 + 4x $$ - $$ 100^{	ext{th}} $$ term: $$ 6 + 99x $$ - Value of $$ x = 3 $$.

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