Question

Write an Arthmetic sequence with third term 34 and sixth term 67.

Answer 1

Answer:

12, 23, 34, 45, 56, 67, . .

Step-by-step explanation:

Let the first term and common difference of the A.P. be a and d respectively.

By given information,

3rd term = 34 and 6th term = 67.

nth term of an A.P. is given by ;

T_n = a + (n - 1) × d

T_3 = a + (3 - 1) × d => a + 2d = 34..(i)

T_6 = a + (6 - 1) × d => a + 5d = 67..(ii)

Now, subtracting (ii) from (i), we get,

3d = 33 => d = 11

Substituting d = 11 in (i), we have,

a + 2 × 11 = 34

a = 34 - 22 = 12

Hence, the arithmetic sequence is,

12, 23, 34, 45, 56, 67, . . .