Exercise 5.4: AP Word Problems (Optional)

Which of the following sequences is an Arithmetic Progression (AP)?

How many terms are there in the AP: 7, 13, 19, ..., 205?

For an AP, if the first term is 'a' and the common difference is 'd', which of the following statements is INCORRECT?

Consider an AP with first term 'a' and common difference 'd'. If the sum of its first 10 terms is 100, the sum of its last 15 terms is 375, and the last term is 39, find the first term 'a'.

The sum of three numbers in an AP is `24` and their product is `440`. What are the numbers?

If the sum of the first m terms of an AP is equal to the sum of the first n terms (where m ≠ n), then the sum of its first (m + n) terms is:

For an Arithmetic Progression, if the first term a > 0 and the common difference d < 0, what is the maximum possible sum of its terms?

Consider the sequence given by a_n = 3n - 5. Is this an Arithmetic Progression? If so, what is its common difference?

Which of the following sequences is an Arithmetic Progression (AP)?

A spiral is made up of successive semicircles, with centers alternately at A and B, starting with center A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... What is the total length of such a spiral made up of 13 consecutive semicircles? (Use π = 22/7).