Math, asked by manyasanthosh123, 4 months ago

arithmetic progression important question and answers class 10​

Answers

Answered by prajapatijigar656
0

Answer:

An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant. For example, the sequence 1, 2, 3, 4, ... is an arithmetic progression with common difference 1. Second example: the sequence 3, 5, 7, 9, 11,... is an arithmetic progression. with common difference 2

Step-by-step explanation:

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Answered by geeta387001
1

Answer:

Question 1.

Find the common difference of the AP 1p,1−pp,1−2pp,…. (2013D)

Solution:

The common difference,

Question 2.

Find the common difference of the A.P. 12b,1−6b2b,1−12b2b,…. (2013D)

Solution:

The common difference, d = a2 – a1 = 1−6b2b−12b

= 1−6b−12b=−6b2b = -3

Question 3.

Find the common difference of the A.P. 13q,1−6q3q,1−12q3q,…. (2013D)

Solution:

Common difference, d = a2 – a1 = 1−6q3q−13q

= 1−6q−13q=−6q3q = -2

Question 4.

Calculate the common difference of the A.P. 1b,3−b3b,3−2b3b,…. (2013D)

Solution:

Common difference, d = a2 – a1= 3−b

Question 3.

Find the common difference of the A.P. 13q,1−6q3q,1−12q3q,…. (2013D)

Solution:

Common difference, d = a2 – a1 = 1−6q3q−13q

= 1−6q−13q=−6q3q = -2

Question 4.

Calculate the common difference of the A.P. 1b,3−b3b,3−2b3b,…. (2013D)

Solution:

Common difference, d = a2 – a1= 3−b3b−1b

= 3−b−33b=−b3b=−13

Question 5.

Calculate the common difference of the A.P. 13,1−3b3,1−6b3,… (2013OD)

Solution:

Common difference, d = a2 – a1 = 1−3b3−13

= 1−3b−13=−3b3 = -b

Question 6.

What is the common difference of an A.P. in which a21 – a7 = 84? (2017OD )

Solution:

a21 – a7 = 84 …[Given

∴ (a + 20d) – (a + 6d) = 84 …[an = a + (n – 1)d

20d – 6d = 84

14d = 84 ⇒ d 8414 = 6

Question 7.

Find the 9th term from the end (towards the first term) of the A.P.    5,9,13, …, 185. (2016D)

Solution:

Here First term, a = 5

Common difference, d = 9 – 5 = 4

Last term, 1 = 185

nth term from the end = l – (n – 1)d

9th term from the end = 185 – (9 – 1)4

= 185 – 8 × 4 = 185 – 32 = 153

Question 8.

The angles of a triangle are in A.P., the least being half the greatest. Find the angles. (2011D)

Solution:

Let the angles be a – d, a, a + d; a > 0, d > 0

∵ Sum of angles = 180°

∴ a – d + a + a + d = 180°

⇒ 3a = 180° ∴ a = 60° …(i)

By the given condition

a – d = a+d2

⇒ 2 = 2a – 2d = a + d

⇒ 2a – a = d + 2d ⇒ a = 3d

⇒ d = a3=60∘3 = 20° … [From (i)

∴ Angles are: 60° – 20°, 60°, 60° + 20°

i.e., 40°, 60°, 80°

Question 9.

Find whether -150 is a term of the A.P. 17, 12, 7, 2, … ? (2011D)

Solution:

Given: 1st term, a = 17

Common difference, d = 12 – 17 = -5

nth term, an = – 150 (Let)

∴ a + (n – 1) d = – 150

17 + (n – 1)(-5) = – 150

(n – 1) (-5) = – 150 – 17 = – 167

(n − 1) = −167−5

n = 1675 + 1 = 167+55=1725

n = 1725 …[Being not a natural number

∴ -150 is not a term of given A.P.

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