If a, b, c are in arithmetic progression, then the value of \(\frac{1}{a} + \frac{1}{c}\) is:

a) \(\frac{2}{b}\)

b) \(\frac{2}{c}\)

c) \(\frac{2}{a}\)

d) \(\frac{1}{b}\)

If the first term of an A.P. is a, the second term is b, and the third term is c, what is the value of b in terms of a and c?

a) \(b=a+c\)

b) \(b=a-c\)

c) \(b=\frac{a+c}{2}\)

d) \(b=\frac{a-c}{2}\)

What is the sum of all the terms from 10 to 90 in an arithmetic progression where the first term is 5 and the common difference is 3?

a) 3000

b) 3100

c) 3200

d) 3300

The sum of first 20 terms of an arithmetic progression is 340. What is the 10th term if the first term is 5?

a) 25

b) 30

c) 35

d) 40

What is the motivation behind studying arithmetic progression (A.P.)?

a) To learn about mathematical patterns.

b) To understand sequences and series.

c) To solve real-world problems involving regular increments or decrements.

d) All of the above.

If the first term of an arithmetic progression is 8 and the 15th term is 68, what is the common difference?

a) 3

b) 4

c) 5

d) 6

How do we apply arithmetic progression in solving daily life problems?

a) Calculating monthly expenses.

b) Determining the amount saved over time with fixed deposits.

c) Predicting future population growth.

d) All of the above.

Which term of the arithmetic progression 3, 7, 11, 15, … is 31?

a) 10th term

b) 11th term

c) 12th term

d) 13th term

In an arithmetic progression, what happens when the common difference ‘d’ is negative?

a) The terms decrease by ‘d’ units as we move forward.

b) The terms increase by ‘d’ units as we move forward.

c) The terms remain constant.

d) The progression becomes irregular.

Which term of the arithmetic progression 3, 7, 11, 15, \(\ldots\) is 31?

a) 10th term

b) 11th term

c) 12th term

d) 13th term