Question

Here are the four of the sequence
23,17,11,5
a) Find the next term
b) Find the (n)th term

Answer 1

Answer:

a)The difference is 6 so subtract 6 from 5(5-6=-1)

therefore the next term is -1

b)a+(n-1)*d

a=first number in the sequence

b=difference in the sequence

so 23+(n-1)*(-6)

23-6n+6

-6n+29

therefore the nth term is -6n+29

Answer 2

The next term of the sequence is equal to -1 and the nth term is equal to (29 - 6n).

Given:

The four terms of the sequence are 23, 17, 11, and 5.

To Find:

a) Find the next term

b) Find the nth term

Solution:

a) The given sequence is an arithmetic progression (A.P.). The next term of the A.P. is equal to the previous term decreased by 6.

∴ The first term (a) of this A.P. is 23 and the common difference (d) is equal to -6.

→ The next term of the sequence would be equal to 5 decreased by 6.

∴ The next term of the A.P. = 5 - 6 = -1.

∴ The next term of the A.P. would be equal to -1.

b) The first term of the A.P = a

   The second term of the A.P = a + d = a + (2 - 1)d

   The third term of the A.P = a + 2d = a + (3 - 1)d

   The fourth term of the A.P = a + 3d = a + (4 - 1)d

→ Therefore on following the above pattern, the nth term would be equal to a + (n-1)d.

                                ∴ nth term (Tₙ) = a + (n - 1)d

                                ∴ nth term (Tₙ) = 23 + (n - 1)(-6)

                                ∴ nth term (Tₙ) = 23 - 6n + 6

                                ∴ nth term (Tₙ) = 29 - 6n

Therefore the next term of the sequence is equal to -1 and the nth term is equal to (29 - 6n).

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