Question

x − 1, x, x + 1, x + 2 · · · are in an arithmetic sequence. a) What is the common difference of this sequence ? b) Write the algebraic form of this sequence c) Write some more terms of this sequence d) If the product of first and third terms of this sequence is 15, what is its first term?

Answer 1

Answer: common difference = x+1-x

d= 1

algebraic form

x_n =dn+(f-d)

=1n+(x-1 -1)

=n+x-2

other term

x+3,x+4,x+5

(x-1)(x+1)=15

x^2+x-x-1=15

x^2-1=15

x^2=16

x=+-4

therefore first term

x-1 =4-1 or -4-1

=3 or -5

algebraic form

x_n =n+4-2 or n-4-2

=n+2 or n-6

Step-by-step explanation:

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Answer 2

Answer:

answers for the given problems are given