Question

in the Arithmetic sequence 10 16 22 to the sum of any two terms be a term of the sequence justify the product of any two terms be a term of sequence justify the squares of all times of the sequence can be term of the sequence justify​

Answer 1

a(1) = 10

a(2) = 16 = 10 + 2*2 = a(1) + 2*2

a(3) = 22 = 106+ 2*3 = a(2) + 2*3 = 10 + 2*(2+3)

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So The sequence goes on like this:

a(n) = a(n -1) + 2*n = a(1) + 2*((n(n+1)/2) - 1) = 10 + 2*((n(n+1)/2) - 1)

a(p) + a(q) = 2*10 + 2*((p(p+1)/2) +(q(q+1)/2) - 2)

a(p) - a(q) = p(p+1) - q(q+1)

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Answer 2

Answer:

in the Arithmetic sequence 10 16 22 to the sum of any two terms be a term of the sequence justify the product of any two terms be a term of sequence justify the squares of all times of the sequence can be term of the sequence justify