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Arithmetic Progressions

Long Answer Type

261.
In which of the following situations, does the list of numbers involved make an arithmetic progression and why ?

(i) The height (in cm) of some students of a school standing in a queue in morning assembly are 147, 148, 149........,157.

(ii) The cash prizes (in Rs.) given by a institute to the papers of class X and XII are respectively, 500, 700, 900, ........ 1700.

(iii) The taxi fare after each km when the fare is Rs. 15 for the first km and Rs. 8 for each additional km.

(iv) The cost of painting the wall of a building, when it costs Rs. 50 for the first metre and rises by Rs. 20 for subsequent metre.

(v) The individual academic fee of the institute when it charge Rs. 500 for the first month and Rs. 100 for each subsequent month.

(i) Here, 147, 148, 149,....... 157
a₂ – a₁ = 148 – 147 = 1
a₃ – a₂ = 149 – 148 = 1
Since, the difference between each pair of consecutive terms are constant.
So, the given numbers form an A .P.
(ii) Here, 500, 700, 900,.......... 1700
a₂ – a_x = 700 – 500 = 200
a₃ – a₂ = 900 – 700 = 200
Since, the difference between each pair of consecutive terms are constant.
So, the given numbers form an A .P.
(iii) Here,
Taxi fare for first km = 15
for second km = 15 + 8=23
for third km = 23 + 8 = 31
So, we have 15, 23, 31,...........
Since, the difference between each pair of consecutive terms are 8.
So, the given numbers form an A .P.
(iv) Cost of painting the wall of building for
First metre = 50
Cost of painting the wall of building for
2nd metre = 50 + 20 = 70
Cost of painting the wall of building for
3rd metre = 70 + 20 = 90
So, we have 50, 70, 90,...........
Since, the difference between each pair of consecutive terms are 20.
So, the given numbers form an A .P.
(v) The academic fees for
Ist month = 500
Fees for 2nd month = 500 + 100 = 600
Fees for 3rd month = 600 + 100 = 700
So, we have 500, 600, 700,...........
Since, the difference between each pair of consecutive terms are 100.
So, the given numbers form an A .P.

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262. Write first four terms of the A .P., when the first term a and the common difference d are given as follows :

(i) a = 10, d = 10.
(ii) a = –1, d = 1/2
(iii) a = –1.25, d = 0.25.
(iv) a = p, d = –3q.
(v) a = b, d = 2c.

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Short Answer Type

263.

Find the next term of the A. P.
Which term of the A.P. 21, 18, 15.....is zero?

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264.

Which term of the A .P. 14, 11, 8..... is - 1?

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265.

(i) For what value of p, are 2p – 1,7 and 3p, three consecutive terms of an A . P. ?

(ii) For what value of p are 2p + 1, 13, 5p –3, three consecutive terms of an A . P. ?

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266.

Find the 10th term from the end of the following A .P. :
(i) 1. 6, 11, 16............201
(ii) 3, 6, 9, 12........... 102

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267. In an A .P., the First term is 8, n^th term is 33 and sum to first n terms is 123. Find n and d, the common difference.

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268. The first term of an A .P. is ‘p’ and its common difference is ‘q’ Find its 10^thterm.

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269. (i) In an A .P., the first term is 25, n^thterm is (–17) and sum to first n terms is 60. Find n and d, the common difference.

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270. The nth term of an A .P. is 6n + 2 find its common difference.

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