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Arithmetic Progressions

Short Answer Type

221.

The 10^th term from the end of the A .P., 8,10, 12,........ 126 is
(a) 107 (b) 106 (c) 108 (d) 109

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222.

The first term, common difference and last term of an A .P. are 12, 6 and 252 respectively. The sum of all terms is
(a) 5410 (b) 5411 (c) 5412 (d) 5413

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223.

The sum of all two digit positive numbers divisible by 3 is
(a) 1664 (b) 1665 (c) 1666 (d) 1600

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224. If k^th term of an

straight A. space straight P. space 5 1 half comma space 11 comma space 16 1 half comma space 22 comma space......

is 550 then the value of 'K' is
(a) 99 (b) 101 (c) 100 (d) 102

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225.

If a₆ – a₅ is 200 then the value of a₇ – a₆ of the same A .P. will be
(a) 100 (b) 400 (c) 200 (d) 300

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226.

Find the sum of three numbers is an A .P. is 27 and their product is 405. The numbers are : (a) (3,9,15) (b) (15, 9, 3) (c) both (a) and (b) (d) (3, 9, 12)

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227. The sum of all the natural numbers less than 100 which arc divisible by 6 is (a) 815 (b) 817 (c) 812 (d) 816

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

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Cost of digging the well after 1 metre of digging of Rs. 150 = a₄Cost of digging the well after 2 metres of digging
= Rs. 150 + Rs. 50
= Rs. 200 = a₂Cost of digging the well after 3 metres of digging
= Rs. 150 + Rs. 50

= Rs. 2a = a₃Cost of digging the well after 4 metres of digging
= Rs. 200 + Rs. 50
= Rs. 250 = a₄and so on.
a₂ – a₄ = Rs. 200 – Rs. 150 = Rs. 50
a₃ – a₂ = Rs. 250 – Rs. 200 = Rs. 50
a₄ – a₃ = Rs. 350 – Rs. 250 = Rs. 50
i.e., a_{k +1} – a_k is the same every time.
So this list of numbers forms an A .P. with the first term a Rs. 150 and the common difference d = Rs. 50.

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229. Write first four terms the A .P. when the first term ‘a’ and the common difference ‘d’ are given as follows :

a – 10, d = 10

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230. Write first four terms the A .P. when the first term ‘a’ and the common difference ‘d’ are given as follows :

a = –2, d = 0

98 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

228. In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

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

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.