Mccarthy Spencer
11/27/2023 · Senior High School
Consider the linear number pattem \( 2 x+1 ; 3 x+3 ; 4 x+5 ; \ldots \) (1) Write down the fourth term of the number pattem in terms of \( x \). (2) Express the general term ( \( n \)-th term) in terms of \( x \) and \( n \). (3) If the \( 15^{\text {th }} \) term is 109 , determine the value of \( x \). (4) If \( x=5 \), determine the largest value of \( n \) for which \( T_{n}<158 \).
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1. Fourth term: \( 5x + 7 \)
2. General term: \( T_n = (n + 1)x + (2n - 1) \)
3. Value of \( x \): \( 5 \)
4. Largest \( n \) for \( T_n < 158 \) when \( x = 5 \): \( 21 \)
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