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

a) Calculating the average age of a group.

b) Determining the total distance traveled by a moving object.

c) Finding the number of years required to repay a loan.

d) All of the above.

Which formula represents the nth term of an arithmetic progression?

a) \( a_n = a + (n-1)d \)

b) \( a_n = a + nd \)

c) \( a_n = a \times d^{n-1} \)

d) \( a_n = a \times d^n \)

What does ‘a’ represent in the nth term formula of an A.P.?

a) The common difference.

b) The first term.

c) The last term.

d) The number of terms.

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

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.

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

Which of the following situations is best represented by an arithmetic progression?

a) Growth of bacteria population.

b) Depreciation of car value.

c) Annual salary increment.

d) Fluctuating stock prices.

The sum of first n terms of an A.P. is \(3n^2 + 2n\). What is the nth term of the A.P.?

a) 3n

b) 6n + 2

c) 3n + 2

d) 6n

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

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