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

For the arithmetic progression (A.P.): \(10, 7, 4, .....\)
The first term is \(a = 10\).
The common difference is \(d = a_2 - a_1 = 7 - 10 = -3\).
The formula for the nth term of an A.P. is \(a_n = a + (n - 1) d\).
To find the 30th term (\(a_{30}\)):
\(a_{30} = 10 + (30 - 1) (-3)\)
\(a_{30} = 10 + (29) (-3)\)
\(a_{30} = 10 - 87\)
\(a_{30} = -77\)

Therefore, the correct option is (C): \(-77\).