Question

Find: 

(i) the 20th term of the AP 9,13,17,21,.......... 

(ii) the 35th term of AP 20,17,14,11,..........

(iii) the 18th term of the AP \(\sqrt{2},\sqrt{18},\sqrt{50},\sqrt{98}\),...........

(iv) the 9th term of the AP \(\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4}\),.........

(v) the 15the term of the AP -40, - 15,10,35,.........

Answer 1

(i) The given AP is 9,13,17,21,..........

First term, a = 9

Common difference, d = 13 - 9 = 4

n^th term of the AP, a_n = a + (n - 1) d = 9 + (n - 1) x 4

∴ 20th term of the AP, a₂₀ = 9 + (20 - 1) x 4 = 9 + 76 = 85

(ii) The given AP is 20,17,14,11,.......... 

First term, a = 20 

Common difference, d = 17 - 20 = - 3

n^th term of the AP, a_n = a + (n - 1) d = 20 + (n - 1) x (-3)

∴ 35th term of the AP, a₃₅ = 20 + (35 - 1) x (-3) = 20 - 102 = -82

(iii) The given AP \(\sqrt{2},\sqrt{18},\sqrt{50},\sqrt{98}\),...........

This can be re-written as \(\sqrt{2},3\sqrt{2},\sqrt{2},5\sqrt{2},7\sqrt{2}\),.........

First term, a = \(\sqrt{2}\)

Common difference, \(d=3\sqrt{2}-\sqrt{2}=2\sqrt{2}\)

(iv) The given AP is \(\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4}\),.........

First term, a = \(\frac{3}{4}\)

(v) The given AP is -40, -15,10,35,.........

First term, a = -40

Common difference, d = -15-(-40) = 25

n^th term of the AP, an = a + (n - 1) d = -40 + (n - 1) x 25