a) Write the sequence got by adding one to the square of consecutive natural numbers starting from 1
b) What is the 10th term of this sequence? c) Write the algebraic form of this sequence?
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Answers
Given : sequence got by adding 1 to the square of consecutive natural numbers starting from 1
To Find : the sequence
10th term of this sequence
the algebraic form of this sequence
Solution:
adding 1 to the square of consecutive natural numbers starting from 1
Tₙ = n² + 1
n = 1
=> T₁= 1² + 1 = 2
n = 2
=> T₂= 2² + 1 = 5
n = 3
=> T₃= 3² + 1 = 10
n = 4
=> T₄= 4² + 1 = 17
n = 5
=> T₅= 5² + 1 = 26
n = 6
=> T₆= 6² + 1 = 37
Hence sequence is
2 , 5 , 10 , 17 , 26 , 37 and so on
Tₙ = n² + 1
n = 10
=> T₁₀ = 10² + 1 = 101
the algebraic form of this sequence n² + 1 n∈ natural numbers
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Required sequence is 12+1, 22+1, 32+1, 42+1, .... 10th term of sequence is a10 = 102+1 = 100+1 = 101.