The average of an Arithmetic progression with $151$ terms is zero. One of its terms is zero.

Which term of the Arithmetic Progression is zero? Show your steps.

Huner said, "The value of the $20$th term of ANY arithmetic progression is double that of the $10$th term."

Is Huner's statement correct? Justify your answer.

Shivam bought a large quantity of marigold flowers to decorate his house for a family function. He used $630$ flowers to recreate the pattern shown below. He used $7$ flowers in the shortest garland and $35$ flowers in the longest garland.

If he kept the difference between two consecutive garlands the same, how many garlands did he make? Show your steps.

Parth was receiving spam calls from a telemarketing centre. He got the first call at $2:48 \mathrm{pm}$ as shown below.

If the telemarketer continues to call using the same pattern, at what time will Parth receive the $13$th call? Show your work.

Ramit is moving towards a stationary object of sound at a constant speed. At his initial position, he hears a pitch of $5$ hertz.

If the pitch from the source increases by $4$ hertz for every $5$ m Ramit travels, find the distance he would have travelled towards the source when the pitch is exactly $149$ hertz. Show your steps.

A stone is thrown into still water and the figure below represents the concentric circular phenomenon known as ripple effect. The radius of first circle is $3$ cm.

If the radius of each subsequent circle is $4$ cm more than the previous, which circle has a radius of $43$ cm? Show your steps.

$14,21,28,25,...$and $26,39,52,65,..$are two arithmetic progressions such that the $p$th term of the first arithmetic progression is the same as the $q$th term of the second arithmetic progression.

Derive a relationship between $p$ and $q$. Show your work.

Animation is a method in which a sequence of images are manipulated to appear as moving objects. An animation specialist wants to show the growth of a sapling into a tree through animation. She follows the steps below:

• She develops the first image by designing a sapling containing a certain number of leaves.
• She develops the second image by adding $15$ leaves to the first image.
• She develops the third image by adding $22$ leaves to the second image.
• She develops the fourth image by adding $29$ leaves to the third image and so on.

If she continues the process in the same manner, how many leaves will she be adding to the $25$th image to develop $26$th image? Show your work.

The sum of first two terms of an arithmetic progression is the same as the sum of the first seven terms of the same arithmetic progression.

Can such an arithmetic progression exist? Justify your answer,