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Answered on 01 Mar Learn Arithmetic Progression
Kalaiselvi
Online Mathematics tutor with 4 years experience(Online Classes for 10th to 12th)
Lesson Posted on 08/06/2022 Learn Arithmetic Progression
Arithmetic Progression Example
Ashish K Sharma
I was a teacher and author and now, I am a Scientist. I have a PG degree in Mathematics as well a Diploma...
Arithmetic Progression Example.
Q:If the sum of the first 7 terms of an AP is 49 and that of the first 17 terms is 289,find the sum of its first n terms.
Solution:
We know that the Sum of the first n terms of an AP is given by:
Sn = (n / 2) * ((2 * a + (n-1) * d)).
Therefore, as per the first requirement,
49 = (7 / 2) * ((2 * a + (7-1) * d)).
Similarly, as per the second requirement,
289 = (17 / 2) * ((2 * a + (17-1) * d)).
Now, from (1), we have , a = 7 – 3d. Substituting this value of a in (2), we have
17 = 7-3d + 8d
Whence, 10 = 5d,
Thus, d = 2.
And, then a is 7 – (3 * 2) = 7 – 6 = 1
Thus, we have, a = 1 and d = 2. Now, the sum of the first n terms is
Sn = (n / 2) * ((2 * a + (n-1) * d)).
Thus,
The sum of its first n terms = n^2.
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Answered on 16 Apr Learn Arithmetic Progression
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