Question

Choose the correct choice in the following and justify: $30^{th}$ term of the AP: $10, 7, 4,.....$ is

• A. 97
• B. 77
• C. -77
• D. -87

Answer 1

Answer: (C)

-77

Answer 2

Given that,
A.P. $10, 7, 4, .....$
First term, $a = 10$
Common difference, $d = a_2 − a_1 = 7 − 10 = −3$
We know that,
$a_n = a + (n − 1) d$
$a_{30} = 10 + (30 − 1) (−3)$
$a_{30} = 10 + (29) (−3)$
$a_{30}= 10 − 87$
$a_{30}= −77$

Hence, the correct option is (C): $-77$