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Which term of the A.P. 3, 8, 13, 18,.....is 78 ?

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Important Questions on Arithmetic and Geometric Progression

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

The angles of a triangle are in AP (arithmetic progression). If measure of the smallest angle is $50 °$ less than that of the largest angle, then find the largest angle.

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

The number of terms common to both the arithmetic progressions

2, 5, 8, 11, \dots, 179

and

3, 5, 7, 9, \dots, 101

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

The angles of a pentagon are in arithmetic progression.The sum of the smallest and largest angle is

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

If the sum of '

n

' terms of an AP (Arithmetic Progression) is

2 n^{2}

, the fifth term is ______

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

What is the value of

21 + 22 + . . . . . . + 46

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + . . . . . . . + \frac{1}{n (n + 1)} = \frac{99}{100}

then what is the value of

n

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

The sum of third and ninth term of an A.P is

8

. Find the sum of the first

11

terms of the progression.

HARD

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

The common difference of the

A . P . b_{1}, b_{2}, . . . ., b_{m}

2

more than common difference of

A . P . a_{1}, a_{2}, . . . . ., a_{n}

. If

a_{40} = - 159, a_{100} = - 399

and

b_{100} = a_{70}

, then

b_{1}

is equal to :

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

The difference between two numbers is

48

and the difference between their arithmetic mean and their geometric mean is

18

. Then, the greater of two numbers is

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

How many numbers are there from $200$ to $800$ which are neither divisible by $5$ nor by $7$ ?

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

Let

a_{1}, a_{2}, a_{3} . . .

be an

A . P .

with

a_{6} = 2 .

Then, the common difference of this

A . P .,

which maximise the product

a_{1} \cdot a_{4} \cdot a_{5},

is :

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

What will be the

10 t h

number in the series

12, 19, 26, 33,_____?

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

a_{1}, a_{2}, a_{3}, . . . .

are in A.P. such that

a_{1} + a_{7} + a_{16} = 40,

then the sum of the first

15

terms of this A.P is

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

A person saves

₹ 1000

more than he did the previous year. If he saves

₹ 2000

in the first year, in how much many years will he save

₹ 170000

HARD

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

If the sum of the series

20 + 19 \frac{3}{5} + 19 \frac{1}{5} + 18 \frac{4}{5} + . . . . . . . . . .

up to

n^{th}

term is

488

and the

n^{th}

term is negative, then :

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

60

times the

60^{th}

term of an

AP

with non zero common difference is equal to

40

times the

40^{th}

term, then the

100^{th}

term of this

AP

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

Let

α_{r}

be the

r^{th}

term of an A.P. whose first term is

a

and common difference is

d

. If for some positive integers

m, n, m \neq n, α_{m} = \frac{1}{n}

and

α_{n} = \frac{1}{m},

then

a - d

equals

EASY

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

$Let S_{n} = 1 \cdot (n - 1) + 2 \cdot (n - 2) + 3 \cdot (n - 3) + \dots + (n - 1) \cdot 1, n ⩾ 4 .$

$The sum \sum_{n = 4}^{\infty} (\frac{2 S_{n}}{n!} - \frac{1}{(n - 2)!}) is equal to :$

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

R s . 720

was divided among

A, B, C, D

and

E

. The sum received by them was in ascending order and in Arithmetic Progression.

E

received

R s . 40

more than

A

. How much did

B

received?

MEDIUM

Mathematics>Algebra>Arithmetic and Geometric Progression>Introduction to Arithmetic Progression

What is the value of

21 + 24 + 27 + . . . . . + 51

Which term of the A.P. 3, 8, 13, 18,.....is 78 ?

Important Questions on Arithmetic and Geometric Progression

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