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Arithmetic Progressions

Short Answer Type

41.

Find the number of terms in each of the following APs :

$space space space 18 comma space 15 1 half comma space 13 comma space....... comma space minus 47$

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42.

Check whether – 150 is a term of the AP : 11, 8, 5, 2 . .

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43.

Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

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44.

An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

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45. If the 3rd and 9th terms of an A .P. are 4 and -8 respectively, which term is zero?

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46. The 17th term of an A .P. exceeds the 10th term by 7. Find the common difference.

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47.

Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?

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48.
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?

Let the common difference of both the
A.P.’s = d
and First term of Ist A.P. = a
also first term of 2nd A .P. = b
Then, 200th term of 1st A .P. = a + 99d
and 100th term of IInd A .P. = b + 99d
Difference between their 100th term = 100
(given)
⇒ (a + 99d) – (b + 99d) = 100
⇒ a – b = 100 ...(i)
Now, a₁₀₀₀ of Ist A.P. = a + 999d
and a₁₀₀₀ of Ilnd A .P. = b + 999d
Hence, difference between their 1000th terms
= (a + 999d) (b + 999d) = a – b
= 100. [Using (i)]