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

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

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 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

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

In an arithmetic progression, if the sum of the first 10 terms is 120, what is the sum of the next 10 terms?

a) 240

b) 260

c) 280

d) 300

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.

In an arithmetic progression, what does the common difference represent?

a) The difference between any two consecutive terms.

b) The ratio of any two consecutive terms.

c) The product of any two consecutive terms.

d) The sum of any two consecutive terms.

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.

How can we find the sum of the first ‘n’ terms of an arithmetic progression?

a) Using the formula \( S_n = \frac{n}{2} (2a + (n-1)d) \)

b) Adding all ‘n’ terms individually.

c) Multiplying the first and last terms by the number of terms and dividing by 2.

d) Subtracting the last term from the first term.