Question

Find the 20 the term of an ap whose 3 rd term is 7 and 7 the term exceeds three times the third term by 2 .Also find its n the term

Answer 1

Answer:

20 th term = 37

nth term = 2n-3

Step-by-step explanation:

Let say first term = a

Common difference = d

nth term = a + (n-1)d

3rd term = a + (3-1)d

=> 3rd term = a + 2d

7th term = a + 6d

7th term = 3rd term × 3  + 3   given

3rd term = 3 given

7th term = 3 × 3  + 2

=> 7th Term = 11

a + 6d = 11

a + 2d = 3    ( third term)

(a +6d) - (a +2d) = 11 -3

4d = 8

d = 2

a + 2d = 3

a + 2(2) = 3

a = 3 - 4

a = -1

20th term = a + 19d

= -1 + 19(2)

= 37

nth term = a + (n-1)d

= -1 + (n-1)2

= -1 + 2n -2

= 2n-3