Question

Write the m th term of the AP 1/k,1+k/k,1+2k,....

Answer 1

I think AP must be this ...
so according 2 it I have answered

Answer 2

Answer:

Step-by-step explanation:

Let Tm be the mth term of an Ap.

The mth term is given by the following formula:

Tm = a + d(m - 1)

a = The first term

d = common difference

m = The number of terms.

We need to get the common difference .

Given a, b , c as an arithmetic progression a being the first term , b the second and c the third , The common difference is given as follows :

b -a = c - b

(1 + k)/k - 1/k = 1 + 2k - (1 + k)/k

Multiply through by k:

1 + k - 1 = k + 2k² - 1 - k

k = 2k² - 1

2k² - k - 1 = 0

the roots are :

-2 and 1

Expanding we have :

2k² - 2k + k - 1 = 0

2k(k - 1) + 1(k - 1) = 0

(2k + 1)(k - 1) = 0

k = 1 or -1/2

We take the positive value which is 1.

now :

a = 1

b = (1 + 1)/1 = 2

c = 1 + 2 × 1 = 3

d = 1

The mth term is given by :

Tm = 1 + 1(m - 1)