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.justify ur answer
Answers
Answer:
25th term is 120 more than 15th term.
Step-by-step explanation:
AP: 5, 17, 29, 41 .....
d = 17 - 5 = 12
Let us assume that the X term is 120 more than 15th term.
The difference between Xth term and 15th Term = (X - 15)*d.
Given that above difference is 120.
So
(X - 15)*d = 120
(X - 15)*12 = 120
X = 120/12 + 15 = 25.
So 25th term is 120 more than 15th term.
Let us justify the answer.
15th term = 5 + (15 - 1)* 12 = 173
25th term = 5 + (25 - 1)* 12 = 293
Difference = 293 - 173 = 120.
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 i.e., 12 in each successive term till the 15th term isn't achieved and after that adding 240 in it as:
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
and Fifteenth term = 161 + 12 = 173
NOW, 120 more than its 15th term: 173+120= 293
Again 120/12 = 10
So, after 15th term, 10 more terms are added to get the term which is 120 more than the 15th term.
Hence, the required term = 15 + 10 = 25th term
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