Fill in the blanks in the following table, given that a is the first term, d the commondifference and the nth term of the AP:











(i)


(ii)


(iii)


(iv)


(v)



7


-18


…


-18.9


3.5



3


…


-3


2.5


0



8


10
18


…


105



…


0


-5


3.6


….


(i) Given: a = 7, d = 3 and n = 8,


an = ?


We know:


an = a + (n – 1)d


Thus, an = 7 + (8 – 1)3 = 7 + 21 = 28


(ii) Given a = - 18, n = 10, an = 0, d = ?


We know that an = a + (n – 1)d


Thus, 0 = - 18 + (10 – 1)d


0 = - 18 + 9d


Or, 9d = 18


Or, d = 18/9 = 2


(iii) Given d = - 3, n = 18, an = - 5, a = ?


We know that, an = a + (n – 1)d


Or, - 5 = a + (18 – 1) (- 3)


Or, - 5 = a – 51


Or, a = - 5 + 51 = 46


(iv) Given a = - 18.9, d = 2.5, an = 3.6, n = ?


We know that, an = a + (n – 1)d


Or, 3.6 = – 18.9 + (n – 1)2.5


Or, 2.5(n – 1) = 3.6 + 18.9 = 22.5


n – 1 = 22.5/2.5 = 9


n = 9 + 1 = 10


(v) Given that a = 3.5, d = 0, n = 105, an= ?


We know:,


an = a + (n – 1)d


an = 3.5 + (104 – 1)0


an = 3.5 + 0


= 3.5


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