Question

_ ,18,_,28 are the 4 consicutive terms of an arithmatic sequence find the first term and third term​

Answer 1

Answer:

1st term is 13  & 3rd term is 23  

Step-by-step explanation:

In an arithmetic sequence,nth term = a + (n-1)d

Here, a = 1st term

         n = number of term

         d = common difference

Now, in the arithmetic series _,18,_ 28,

2nd term=18 = a + (2-1)d = a + d ---------(i)

4th term = 28 = a + (4-1)d = a + 3d -----------(ii)

Now, subtracting equation (i) from (ii),

                   a  +  3d     =      28

                ₍₋₎a  + ₍₋₎ d     = ₍₋₎   18

                           2d     =       10

                        ∴   d     =        5

Putting the value of d in equation (i),

                 a + 5 = 18

             ⇒  a      = 18 -5

              ∴  a       = 13

   ∴ 1st term = 13

   ∴ 3rd term = a + (3-1)d = 13 + 2× 5 = 13 + 10 = 23

Therefore, 1st and 3rd terms of the sequence are 13 and 23 respectively.