Nootan solutions for माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 9 - Arithmetic and geometric progression [Latest edition]

For the given A.P.s, write the first term a and common difference d.

3, 5, 7, ....

For the given A.P.s, write the first term a and common difference d.

4, −1, −6, ....

For the given A.P.s, write the first term a and common difference d.

1.7, 2.3, 2.9, ...

Write the first four terms of the A.P. when the first term a and the common difference d are given.

a = 5, d = 2

Write the first four terms of the A.P. when the first term a and the common difference d are given.

a = 3, d = 0

Write the first four terms of the A.P. when the first term a and the common difference d are given.

a = −4, d = −1

Write the first four terms of the A.P. when the first term a and the common difference d are given.

a = `1/2`, d = `3/2`

The following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms.

1²,2², 3², 4²,...

The following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms.

3, 10, 17, 24,...

The following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms.

3, 0, −3, −6,...

The following lists of numbers form an A.P.? If they form an A.P., find the common difference d and write the next three terms.

3, 3, 5, 5,....

If 2k, 3k + 1, and 5k − 1 are three consecutive terms of an A.P., find the value of k.

If 11, a, b, 2, are in A.P., find the values of a and b.

The nth term of a progression is (3n + 5). Prove that this progression is an arithmetic progression. Also, find its 6th term.

The nth term of a progression is (3 – 4n). Prove that this progression is an arithmetic progression. Also, find its common difference.

The nth term of a progression is (n² − n + 1). Prove that it is not an A.P.

Find the 10th term of the progression 1 + 3 + 5 + 7 + ...

Find the 7th term of the progression 80 + 77 + 74 + ...

Find the 22nd term of the progression `7 3/4 + 9 1/2 + 11 1/4 + ...`

Find the nth term of the progression − 5 − 3 − 1 + 1 + ...

Which term of the progression 4 + 8 + 12 + ... is 76?

Which term of the progression 36 + 33 + 30 + ... is zero?

Which term of the progression `3/4 + 1 + 5/4 + ...` is 12?

Find the 16th term from the end of the progression 3 + 6 + 9 + ... + 99.

Find the 10th term from the end of the progression
82 + 79 + 76 + … + 4.

Find the 10th term from the end of the progression 5 + 2 − 1 − 4 − ... − 34.

How many numbers of two digit are divisible by 3?

How many numbers of three digits are divisible by 9?

Find the value of ‘x’ if x + 1, 2x + 1, and x + 7 are in A.P. Also, find the 4th term of this progression.

If k + 3, 2k + 1, k + 7 are in A.P., then find this progression up to 5 terms.

The 3rd and 19th terms of an A.P. are 13 and 77, respectively. Find the A.P.

The 5th and 8th terms of an A.P. are 56 and 95, respectively. Find the 25th term of this A.P.

The pth and qth terms of an A.P. are q and p, respectively. Prove that its (p + q)th terms will be zero.

If (p + 1) th term of an A.P. is twice the (q + 1)th term, then prove that (3p + 1)th term willbe twice the (p + q + 1)th term.

The 12th term of an A.P. is 14 more than the 5th term. The sum of the first three terms is 36. Find the A.P.

Is 303, a term of the progression 5, 10, 15, ...?

Is 38, a term of the progression −18, −14, −10, ....?

Prove that the sum of nth term from the beginning and nth term from the end of an A.P. is constant.

In an A.P., prove that: `T_(m + n ) + T_(m - n) = 2.T_m`

10 times the 10th term and 15 times the 15th term of an A.P. are equal. Find the 25th term of this A.Р.

17 times the 17th term of an A.P. is equal to 18 times the 18th term. Find the 35th term of this progression.

Which term of the progression `10, 9 1/3, 8 2/3,...` is the first negative term?

Which term of the progression `4, 3 5/7, 3 3/7,` is the first negative term?

Each of two arithmetic progressions 2, 4, 6, ... and 3, 6, 9, ... is taken up to 200 terms. How many terms are common in these two progressions?

Find three numbers in A.P. whose sum is 9 and the sum of their squares is 35.

Find three numbers in an A.P. whose sum is 21 and the product of the last two numbers is 63.

Find three numbers in an A.P. whose sum is 12, and product is 60.

Find three numbers in A.P. whose sum is 9 and sum of whose cubes in 99.

The internal angles of a triangle are in A.P. If the smallest angle is 45°, find the remaining angles.

Find 4 numbers in A.P. whose sum is 4 and sum of whose squares is 84.

Find the sum of 50 terms of the A.P. 1 + 4 + 7 + ..... .

Find the sum of 25 terms of the A.P. 8 + 5 + 2 + .... .

Find the sum of the first 200 even natural numbers.

Find the sum of all numbers lying between 201 and 424 which are divisible by 5.

Find the sum of all numbers from 1 to 200 which are divisible by either 2 or 3.

Find the sum of all odd numbers lying between 101 and 200 which are divisible by 3.

Find the sum of all even numbers between 50 and 100 using a formula.

Find the value of x if 1 + 6 + 11 + ... + x = 189.

Find the value of x if 3 + 6 + 9 + ... + 96 = x.

How many terms of the A.P. 6 + 10 + 14 + ... has the sum 880?

How many terms of the A.P. 3 + 9 + 15 + ... has the sum 7500?

The sum of ‘n’ terms of a progression is n(n + 1). Prove that it is an A.P. Also, find its 10th term.

The sum of ‘n’ terms of a progression is (3n² − 5n). Prove that it is an A.Р.

If the sum of ‘n’ terms of a series is (5n² + 3n), then find its first five terms.

The sum of 5 and 15 terms of an A.P. are equal. Find the sum of 20 terms of this A.P.

The sum of 20 and 28 terms of an A.P. are equal. Find the sum of 48 terms of this A.P.

The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.

The sum of 15 terms of an A.P. is zero. Its 4th term is 12. Find its 14th term.

The common difference, last term, and sum of terms of an A.P. are 4, 31, and 136, respectively. Find the number of terms.

In an A.P., the 4th and 6th terms are 6 and 14, respectively. Find the sum of its 20 terms.

The 6th term of an A.P. is equal to 4 times its first term, and the sum of the first 6 terms is 75. Find the first term and the common difference.

In an A.P., if T₁ + T₅ + T₁₀ + T₁₅ + T₂₀ + T₂₄ = 225, find the sum of its 24 terms.

The nth term of an A.P. is (5n − 1). Find the sum of its ‘n’ terms.

The sum of 8 terms of an A.P. is 64, and the sum of 17 terms is 289. Find the sum of its ‘n’ terms.

In an A.P., T₁₂ = 37, d = 3, find a and S₁₂.

The sum of 15 terms of an A.P. is zero, and its 5th term is 12. Find its 12th term.

The nth term of an Arithmetic Progression (A.P.) is given by the relation T_n = 6(7 − n). Find:

1. its first term and the common difference
2. sum of its first 25 terms

The n^th term of a progression is `3^(n + 1)`. Show that it is a G.P. Also, find its 5th term.