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Arithmetic Progressions

Short Answer Type

41.
Find the number of terms in each of the following APs :

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

bold space bold space bold space bold 18 bold comma bold space bold 15 bold 1 over bold 2 bold comma bold space bold 13 bold comma bold space bold. bold. bold. bold. bold. bold. bold. bold comma bold space bold minus bold 47

Here, a= 18

straight d space equals space 15 1 half minus 18 equals 31 over 2 minus 18 equals negative 5 over 2

And, a_n= -47
Let the number of terms be n.
Then, a_n= -47

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a + (n - 1)d = - 47

rightwards double arrow space 18 plus left parenthesis straight n minus 1 right parenthesis open parentheses fraction numerator negative 5 over denominator 2 end fraction close parentheses equals negative 47 rightwards double arrow space space fraction numerator negative 5 over denominator 2 end fraction left parenthesis straight n minus 1 right parenthesis equals negative 47 minus 18 rightwards double arrow space space space space fraction numerator negative 5 over denominator 2 end fraction left parenthesis straight n minus 1 right parenthesis equals negative 65 rightwards double arrow space space space space space 5 over 2 left parenthesis straight n minus 1 right parenthesis space equals space 65 rightwards double arrow space space straight n minus 1 space equals space fraction numerator 65 cross times 2 over denominator 5 end fraction rightwards double arrow space space straight n space minus space 11 space equals space 26 rightwards double arrow space space straight n space equals space 26 space plus space 1 space rightwards double arrow space space straight n space equals space 27

Hence, the number of terms of the given A .P. is 27.

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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?

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49. How many three-digit numbers are divisible by 7?

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50. How many multiples of 4 lies between 10 and 250?

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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

41.
Find the number of terms in each of the following APs :

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