Find 18 t h term of the A.P. 2 , 3 2 , 5 2 …

Here, First term a = 2 Common difference of the A.P. d = 3 2 - 2 = 2 2 Now, as we know, a n = a + n - 1 d So, for 18 t h term, a 13 = a + 18 - 1 d = 2 + 17 2 2 = 2 + 34 2 = 35 2 Therefore, the 18 t h term of the given A.P. is a 18 = 35 2 .

Find 9 t h term of the A.P. 3 4 , 5 4 , 7 4 , 9 4 , … .

Given A.P. is 3 4 , 5 4 , 7 4 , 9 4 , … Here, First term a = 3 4 Common difference of the A.P. d = 5 4 - 3 4 = 5 - 3 4 = 2 4 Now, as we know, a n = a + n - 1 d So, for 9 t h term, a 9 = a + 9 - 1 d = 3 4 + 8 2 4 = 3 4 + 16 4 = 19 4 Therefore, the 9 t h term of the given A.P. is a 9 = 19 4 .

Which term of the A.P. 3 , 8 , 13 , … . i s 248 ?

Let, a n = 248 . a = 3 Now, Common difference d = a 1 - a = 8 – 3 = 5 Thus, using the below mentioned formula a n = a + n - 1 d 248 = 3 + ( n – 1 ) 5 248 – 3 = 5 n – 5 245 + 5 = 5 n ⇒ n = 250 5 n = 50 Therefore, 248 is the 50 t h term of the given A.P.