Find the 18 t h term of the A P 2 , 18 , 50 , 98 , . . . . . . . . . . . .

We are given the A P 2 , 18 , 50 , 98 , . . . . . . . . . . . . This can be re-written as 2 , 9 × 2 , 25 × 2 , 49 × 2 , . . . . . . . . . . . . or 2 , 3 2 , 5 2 , 7 2 , . . . . . . . . . . . . Here, First term a = 2 Second term a 2 = 3 2 Common difference d = 3 2 - 2 = 2 2 We know that a n = a + n - 1 d To find 18 t h term, take n = 18 a 18 = 2 + 18 - 1 2 2 = 2 + 34 2 = 35 2 Hence, 18 t h term of the A P is a 18 = 35 2

Find the 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 d = 5 4 - 3 4 = 2 4 = 1 2 We know that nth term of an A P is given by a n = a + ( n - 1 ) d To find 9 t h term, we have n = 9 a 9 = 3 4 + ( 9 - 1 ) 1 2 = 3 4 + 4 = 3 + 16 4 = 19 4 Hence, 9 t h term of the A P is 19 4

Find the 37 t h term of the A P 6 , 7 3 4 , 9 1 2 , 11 1 4 . . . . . . . . . . . .

We are given the A P is 6 , 7 3 4 , 9 1 2 , 11 1 4 . . . . . . . . . . . . Here, first term a = 6 Second term a 2 = 7 3 4 common difference d = 7 3 4 - 6 = 31 4 - 6 = 31 - 24 4 = 7 4 We know that nth term of an A P is given by a n = a + n - 1 d Now, to find 37 t h term, take n = 37 a 37 = 6 + 37 - 1 7 4 = 6 + 36 × 7 4 = 6 + 63 = 69 Hence, a 37 = 69