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

The Correct Option is C

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): \(-77\)