Ramkali saved Rs. 5 in the first week of a year and then increas

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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.

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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.

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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.

Weekly savings of Ramkali is following :
5, 6.75, 8.50, 10.25............
Here, a = 5, d = 1.75, T_n = 20.75
We know that, T_n= a + (n - 1) d
$rightwards double arrow$ 20.75 = 5 + (n - 1) (1.75)
$rightwards double arrow$ 20.72= 5 + 1.75 n - 1.75
$bold rightwards double arrow$ 20.75 = 1.7n + 3.25
$rightwards double arrow$ 1.75n = 17.5

$rightwards double arrow$ $straight n equals fraction numerator 17.5 over denominator 1.75 end fraction equals 10$

Hence, n = 10.

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56.

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

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57.

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

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58.

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

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59.

Find the sum of the following APs:

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

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60. Find the sums given below:

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