nth term of 4 + 9 + 14 + …………….. is A) 5n +1 B) 4n – 1

1.	nth term of 4 + 9 + 14 + …………….. is A) 5n +1 B) 4n – 1 C) 5n – 1 D) 4n + 1
Answer» Correct option is (C) 5n – 1 Let \(a_1=4,a_2=9,a_3=14\) \(\because\) \(a_2-a_1\) \(=9-4=5\) and \(a_3-a_2\) \(=14-9=5\) \(\because\) \(a_3-a_2\) \(=a_2-a_1\) \(\therefore\) 4, 9, 14, ......... will form an A.P. whose first term is \(a=a_1=4\) & common difference is \(d=a_2-a_1=9-4=5\) \(\therefore\) \(n^{th}\) term of A.P. is \(a_n=a+(n-1)d\) \(=4+(n-1)5\) \(=4+5n-5\) \(=5n-1\) Hence, \(n^{th}\) term of 4+9+14+..….. is \(5n – 1.\) Correct option is C) 5n – 1

nth term of 4 + 9 + 14 + …………….. is A) 5n +1 B) 4n – 1 C) 5n – 1 D) 4n + 1

Answer»

Correct option is (C) 5n – 1

Let \(a_1=4,a_2=9,a_3=14\)

\(\because\) \(a_2-a_1\) \(=9-4=5\)

and \(a_3-a_2\) \(=14-9=5\)

\(\because\) \(a_3-a_2\) \(=a_2-a_1\)

\(\therefore\) 4, 9, 14, ......... will form an A.P. whose first term is \(a=a_1=4\) & common difference is \(d=a_2-a_1=9-4=5\)

\(\therefore\) \(n^{th}\) term of A.P. is \(a_n=a+(n-1)d\)

\(=4+(n-1)5\)

\(=4+5n-5\)

\(=5n-1\)

Hence, \(n^{th}\) term of 4+9+14+..….. is \(5n – 1.\)

Correct option is C) 5n – 1