Choose the correct choice in the following and justify
(i) 30th term of the A.P: 10, 7, 4, …, is
(A) 97 (B) 77 (C) −77 (D.) −87
(ii) 11th term of the A.P. -3, -1/2, ,2 .... is
(A) 28 (B) 22 (C) - 38 (D)
(i) Given that
A.P. 10, 7, 4, …
First term, a = 10
Common difference, d = a2 − a1 = 7 − 10 = −3
We know that, an = a + (n − 1) d
a30 = 10 + (30 − 1) (−3)
a30 = 10 + (29) (−3)
a30 = 10 − 87 = −77
Hence, the correct answer is option C.
(ii) Given that A.P. is -3, -1/2, ,2 ...
First term a = - 3
Common difference, d = a2 − a1 = (-1/2) - (-3)
= (-1/2) + 3 = 5/2
We know that, an = a + (n − 1) d
a11 = 3 + (11 -1)(5/2)
a11 = 3 + (10)(5/2)
a11 = -3 + 25
a11 = 22
Hence, the answer is option B.
