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

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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.

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56.
Find the sum of the following APs:
2, 7, 12, ... to 10 terms.

Here, a = 2
d = 7 – 2 = 12 – 7 = 5
And, n = 10
We know that,

$space space space space space space straight S subscript straight n equals straight n over 2 left square bracket 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d right square bracket therefore space space straight S subscript 10 equals 10 over 2 left square bracket 2 cross times 2 plus left parenthesis 10 minus 1 right parenthesis cross times 5 right square bracket$
= 5 x [4 + 9 x 5]
= 5 x [4 + 45]
= 5 x 49 = 245

Hence, the sum of First 10 terms of the given
A .P. = 245 F

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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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