10 Question MCQ (including Assertion)

In an AP , if \(d=4, n=7, a_n=4\), then \(a\) is

A set of concentric circles is drawn such that their radii form an AP:
\(3 \mathrm{~cm}, 4 \mathrm{~cm}, 5 \mathrm{~cm}, \ldots\) The area of the ring between two consecutive circles forms a new sequence. This sequence of areas is:

The \(4{ }^{\text {th }}\) term from the end of the AP: \(-11,-8,-5, \ldots, 49\) is

Assertion (A): The sum of the first 20 terms is equal to the sum of the first 30 terms for an AP whose first term is 25 and common difference is -2 .
Reason (R): The sum of terms from the 21st to the 30th is zero.

Assertion (A): If the sum of ' \(n\) ' terms of a sequence is \(3 n^2+2 n\), then the sequence is an AP .
Reason (R): The \(n\)th term of the sequence can be found by \(a_n=S_n-S_{n-1}\). If \(a_n\) is a linear expression in ' \(n\) ', the sequence is an AP.

In an AP representing the daily temperature drop during a cold spell, the 5 th day's temperature was \(10^{\circ} \mathrm{C}\) and the \(10^{\text {th }}\) day's was \(5^{\circ} \mathrm{C}\). What does this imply about the progression?

A worker stacks bricks. The bottom layer has 40 bricks, the next has 38 , and so on, up to the top layer with only 2 bricks. To find the total number of bricks, which AP concept is most direct?

Assertion (A): The list of numbers \(5,5,5,5, \ldots\) is an Arithmetic Progression
Reason (R): A sequence is an AP if its terms continuously increase or decrease.

A freelance designer earns ₹15,000 on her first project. She decides to increase her fee by a fixed amount for each subsequent project. If her fee for the 5th project is ₹23,000, the sequence of her fees forms an AP. The first term ' \(a\) ' is ₹15,000. What does ' \(a\) ' represent?