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Arithmetic Progressions

Short Answer Type

51.

For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

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52.

Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.

189 Views

53. The sum of the 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.

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54. Subba Rao started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year. In which year did his income reach Rs. 7000.

155 Views

55. Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75, if in the nth week, her weekly savings became Rs. 20.75, find n.

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56.

Find the sum of the following APs:
2, 7, 12, ... to 10 terms.

124 Views

57.

Find the sum of the following APs:
–37, –33, –29, . . ., to 12 terms.

226 Views

58.

Find the sum of the following APs:
0.6, 1.7, 2.8, . . ., to 100 terms.

262 Views

59.
Find the sum of the following APs:

$1 over 15 comma space 1 over 12 comma space 1 over 10 comma space..... space to space 11 space terms.$

Here, $straight a space equals space 1 over 15$
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And n =11
We know that,

$straight S subscript straight n equals straight n over 2 left square bracket 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d right square bracket therefore space straight S subscript 11 equals 11 over blank 2 open square brackets 2 cross times 1 over 15 plus left parenthesis 11 minus 1 right parenthesis cross times 1 over 60 close square brackets space space space space space space space space space equals 11 over 2 cross times open square brackets 2 over 15 plus 10 cross times 1 over 60 close square brackets space space space space space space space space space space equals 11 over 2 cross times open square brackets 2 over 15 plus 1 over 6 close square brackets equals 11 over 2 cross times open square brackets fraction numerator 4 plus 5 over denominator 30 end fraction close square brackets space space space space space space space space space space equals 11 over 2 cross times 9 over 30 equals 11 over 2 cross times 3 over 10 equals 33 over 20$

Hence, the sum of first 11 terms of the given $straight A. space straight P. space equals 33 over 20$ .