Write an expression for the n th term of the sequence 2 , 5 , 10 , 17 , 26 , . . . . 2,5,10,17,26,.... 2 , 5 , 10 , 17 , 26 , .... Assume that n begins with 1.A) a n = n + 4 a _ { n } = n + 4 a n = n + 4 B) a n = n 2 + 1 a _ { n } = n ^ { 2 } + 1 a n = n 2 + 1 C) a n = n 3 + 1 a _ { n } = n ^ { 3 } + 1 a n = n 3 + 1 D) a n = n 3 − 2 a _ { n } = n ^ { 3 } - 2 a n = n 3 − 2 E) a n = n 2 − 2 a _ { n } = n ^ { 2 } - 2 a n = n 2 − 2

Question

Write an expression for the n th term of the sequence   2 , 5 , 10 , 17 , 26 , . . . . 2,5,10,17,26,.... 2 , 5 , 10 , 17 , 26 , ....   Assume that n begins with 1.A)    a n = n + 4 a _ { n } = n + 4 a n ​ = n + 4 B)    a n = n 2 + 1 a _ { n } = n ^ { 2 } + 1 a n ​ = n 2 + 1 C)    a n = n 3 + 1 a _ { n } = n ^ { 3 } + 1 a n ​ = n 3 + 1 D)    a n = n 3 − 2 a _ { n } = n ^ { 3 } - 2 a n ​ = n 3 − 2 E)    a n = n 2 − 2 a _ { n } = n ^ { 2 } - 2 a n ​ = n 2 − 2

Romanus Nwankwo · Accepted Answer

Final Answer : B, Explanation :   The given sequence can be represented by the formula   a n = n 2 + 1 a_n = n^2 + 1 a n ​ = n 2 + 1  , where   n n n   is the position of the term in the sequence. This formula generates the sequence as follows: when   n = 1 n=1 n = 1  ,   a 1 = 1 2 + 1 = 2 a_1 = 1^2 + 1 = 2 a 1 ​ = 1 2 + 1 = 2  ; when   n = 2 n=2 n = 2  ,   a 2 = 2 2 + 1 = 5 a_2 = 2^2 + 1 = 5 a 2 ​ = 2 2 + 1 = 5  ; and so on, matching the given sequence.

Write an expression for the n th term of the sequence $2, 5, 10, 17, 26, ....$ Assume that n begins with 1.

A) $a _ { n } = n + 4$
B) $a _ { n } = n ^ { 2 } + 1$
C) $a _ { n } = n ^ { 3 } + 1$
D) $a _ { n } = n ^ { 3 } - 2$
E) $a _ { n } = n ^ { 2 } - 2$

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