Question

The nth term of the sequence 6,17,34,57,86…is of the form an2+bn+c .
Then a=?, b=?, c=?

Answer 1

Answer:

a and b are coefficients and c is the constant term

Answer 2

Given,

• The general form of the sequence is $an^{2} + bn + c$.

• The sequence is given as 6,17,34

To find,

The values of a,b and c.

Solution,

For n = 1, the term in the equation is 6. That is,

    $a1^{2} + b + c = 6$

     $a + b + c = 6$ --eq(1)

For n = 2, the term in the equation is 17 that is,

  $a2^{2} + 2b + c = 17$

     $4a + 2b + c = 17$--eq(2)

For n = 3, the term in the equation is 34 that is,

  $a3^{2} + 3b + c = 34$

     $9a + 3b + c = 34$--eq(3)

We have three equations in three variables. From here, we can find the value of a, b, c.

First, we will eliminate c from the given equations resulting in equations with variables a and b. After finding the value of a and b we can get the value of c as well.

a = 3

b = -10

c = 13

Therefore the values of a,b and c are 3, -10, 13, respectively.