If the sum of 7 terms of an A.P. is 49 and that of 17 terms is 289, find the sum of n terms.
Answers
Answered by
17
Answer:
The sum of n terms is n².
Step-by-step explanation:
Given :
S7 = 49 and S17 = 289
Case 1 :
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
S7 = 7/2 [2a + (7 - 1)d]
49 = 7/2 [2a + 6d]
49 × 2/7 = 2[a + 3d]
7 × 2 × ½ = a + 3d
7 = a + 3d
a + 3d = 7
a = 7 - 3d ………….. (1)
Case 2 :
S17 = 289
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
S17 = 17/2 [2a + (17 - 1)d]
289 = 17/2 [2a + 16d]
289 × 2/17 = 2[a + 8d]
17 × 2 × ½ = a + 8d
a + 8d = 17
(7 - 3d) + 8d = 17
[From eq 1]
-3d + 8d = 17 - 7
5d = 10
d = 10/5
d = 2
On Putting the value of d = 2 in eq (1),
a = 7 - 3d
a = 7 – 3 × 2
a = 7 - 6
a = 1
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
Sn = n/2 [2(1) + (n – 1)2]
Sn = n/2[2 + 2n - 2]
Sn = n/2 × 2 [1 + n – 1]
Sn = n [ n ]
Sn = n²
Hence, the sum of n terms is n².
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Answered by
1
Answer:
n^2
Step-by-step explanation:
7*7=49
17*17=289
n*n=n^2
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