without using the formula for the nth term , find which term of the ap: 5,17,29,41,... will be 120 more than its 15th term?

Asked by sonali garg | 20th Oct, 2013, 07:24: PM

Expert Answer:

Given a.p. series is: 5,17,29,41.

Here, first term = a = 5 and common difference = d = 17 - 5 = 12

Now, we don't have to use the formula for nth term. So, the only way to solve it is by finding the 15th term by adding the common difference.:

Given, first term = a = 5

Second term = 17

Third term = 29

Fourth term = 41

Now, fifth term = 41 + 12 = 53

Sixth term = 53 + 12 = 65

Seventh term = 65 + 12 = 77

Eight term = 77 + 12 = 89

Ninth term = 89 + 12 = 101

Tenth term = 101 + 12 = 113

Eleventh term = 113 + 12 = 125

Twelvth term = 125 + 12 = 137

Thirteenth term = 137 + 12 = 149

Fourteenth term = 149 + 12 = 161

Fifteenth term = 161 + 12 = 173

Now, 240 more than fifteenth term = 173 + 240 = 413

Again, 240 ÷ 12 = 20

So, after 15 th term, 20 more terms are added to get the term which is 240 more than the 15 th term.

Hence, the required term = 15 + 20 = 35 th term

Answered by  | 20th Oct, 2013, 07:31: PM

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