Question 1: Find:

Answer:

Question 2: In an A.P., show that .

Answer:

Let the first term be and the common difference be

Question 3:

Answer:

?

is the term.

?

is the term.

?

is the term.

Question 4:

(i) Is a term of the A.P. ?

(ii) Is a term of the A.P. ?

Answer:

?

Since is not a natural number, is NOT a term in the given A.P.

?

Since is not a natural number, is NOT a term in the given A.P.

Question 5:

Answer:

Let the first negative term is .

Thus the term is the first negative term of the given AP.

Let the real term be

a) for to be real,

b) for to be imaginary,

Question 6:

Answer:

Therefore there are terms in the given A.P.

?

Therefore there are terms in the given A.P.

Question 7: The first term of an A.P. is , the common difference is and the last term is ; find the number of terms.

Answer:

Therefore there are terms in the given A.P.

Question 8: The terms of an A.P. are respectively, find the term.

Answer:

… … … … … i)

… … … … … ii)

Solving i) and ii)

Question 9: If term of an A.P. is zero, prove that its term is double the term.

Answer:

To prove:

Substituting

Question 10: If times the term of an A.P. is equal to times the term, show that term of the A.P. is zero.

Answer:

Now

Question 11: The terms of an A.P. are respectively. Find term.

Answer:

… … … … … i)

… … … … … ii)

Solving i) and ii) we get

Substituting from i) we get

Question 12: In a certain A.P. the term is twice the term. Prove that the term is twice the term.

Answer:

… … … … … i)

To prove:

Substituting from i) we get

Question 13: lf term of an A.P. is twice the term, prove that term is twice the term.

Answer:

… … … … … i)

To prove

Substituting from i)

Question 14: If the term of the A.P. is same as the term of the A.P. find .

Answer:

term of sequence

term of sequence

Question 15: Find the term from the end of the following arithmetic progressions:

Answer:

Question 16: The term of an A.P. is three times the first and the term exceeds twice the third term by . Find the first term and the common difference.

Answer:

… … … … … i)

… … … … … ii)

Substituting in i) we get

Question 17: Find the second term and term of an A.P. whose term is and the term is .

Answer:

Given,

… … … … … i)

… … … … … ii)

Solving i) and ii) we get

Question 18: How many numbers of two-digit are divisible by ?

Answer:

The sequence would be

Therefore there are such numbers which are two digit are divisible by

Question 19: An A.P. consists of terms. If the first and the last terms be respectively, find term.

Answer:

Question 20: The sum of terms of an A.P. is and the sum of the terms is . Find the first term and the common difference of the A.P.

Answer:

Solving i) and ii) we get

Substituting in i) we get

Question 21: How many numbers are there between which when divided by leave remainder ?

Answer:

If a number is divided by and leaves as remainder, it can be represented as

Therefore the sequence would be

Hence there are numbers between which when divided by leave remainder

Question 22: The first and the last terms of an A.P. are respectively. Show that the sum of term from the beginning and term from the end is .

Answer:

Given: first term

Therefore the sum of the two terms

Answer:

Question 24: If are in AP, whose common difference is , show that,

Answer:

are in AP