If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms
Answers
Given:
The sum of the first 7 term of an ap is 49 and 17 term is 289.
Find:
The sum of first n terms
Solution:
The sum of 7 term of an Ap is 49
The sum of 17 term of Ap is 289.
we know that,
The sum of 7 term of an Ap is 49.
=> Sn = n/2 [2a + (n - 1)d]
=> S7 = 7/2 [2a + (7 - 1)d]
=> 49 = 7/2 [2a + 6d]
=> 49 = 7/2 × 2[a + 3d]
=> 49 = 7 [a + 3d]
=> 49/7 = a + 3d
=> 7 = a + 3d..................(i).
The sum of 17 term of Ap is 289.
=> Sn = n/2 [2a + (n - 1)d]
=> S17 = 17/2 [2a + (17 - 1)d]
=> 289 = 17/2 [2a + 16d]
=> 289 = 17/2 × 2[a + 8d]
=> 289 = 17 [a + 8d]
=> 289/17 = a + 8d
=> 17 = a + 8d..................(ii).
Now, Subtracting Eq. (ii) and (i) we get,
=> d = 10/5
=> d = 2
Now, putting the value of d in Eq. (i).
=> a + 3d = 7
=> a + 3 × 2 = 7
=> a + 6 = 7
=> a = 7 - 6
=> a = 1
=> Sn = n/2 [2a + (n - 1)d]
=> Sn = n/2 [2 × 1 + (n - 1) (2)]
=> Sn = n/2 [2 + 2n - 2]
=> Sn = n/2[2n]
=> Sn = n/2 × 2n
=> Sn = 2n²/2
=> Sn = n²
Hence, the sum of first n term is n².
I hope it will help you.
Regards.
Answer:
=> Sn = n/2 [2a + (n - 1)d]
=> S7 = 7/2 [2a + (7 - 1)d]
=> 49 = 7/2 [2a + 6d]
=> 49 = 7/2 × 2[a + 3d]
=> 49 = 7 [a + 3d]
=> 49/7 = a + 3d
=> 7 = a + 3d..................(i).
Step-by-step explanation: