The 9^{th} term of the sequence 0, 3, 8, 15, | vedclass

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Question

(C) The given sequence is $0, 3, 8, 15, 24, 35, \dots$Observe the differences between consecutive terms:$3 - 0 = 3$$8 - 3 = 5$$15 - 8 = 7$$24 - 15 = 9

Vedclass · Accepted Answer

$80$

Vedclass · Answer

(C) The given sequence is $0, 3, 8, 15, 24, 35, \dots$Observe the differences between consecutive terms:$3 - 0 = 3$$8 - 3 = 5$$15 - 8 = 7$$24 - 15 = 9$$35 - 24 = 11$The differences are consecutive odd numbers: $3, 5, 7, 9, 11, \dots$To find the $9^{th}$ term,we continue the pattern:$7^{th}$ term $= 35 + 13 = 48$$8^{th}$ term $= 48 + 15 = 63$$9^{th}$ term $= 63 + 17 = 80$Alternatively,the $n^{th}$ term of the sequence is given by $a_n = n^2 - 1$.For $n = 9$,$a_9 = 9^2 - 1 = 81 - 1 = 80$.

The $9^{th}$ term of the sequence $0, 3, 8, 15, 24, 35, \dots$ is

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