Question

The 6th and 11th terms of an arithmetic sequence are 38 and 73.find the first term and write the algebric expression of the sequence​

Answer 1

Step-by-step explanation:

a6 = 38.

a + 5d = 38

a = 38 - 5d.......equation 1

a11 = 73.

a + 10d = 73

38 - 5d + 10d = 73........from equation 1

38 + 5d = 73

5d = 73 - 38

5d = 35

d = 35/5

d = 7

Put d = 7 in equation 1

a = 38 - 5 (7)

a = 38 - 35

a = 3

Therefore ; the first term (a) = 3

a2 = a+d a3 = a +2d. a4 = a + 3d

= 3+7 = 3 + 2(7). = 3 + 3(7)

= 10. = 3 + 14. = 3 + 21

= 17. = 24

Therefore :the A.P. is 3, 10, 17, 24