The best way for solving the problem of arithmetic progressions of ncert of exercise 5.3. How i solve this problem please guide me the best way 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.
AnilSinghBoraGuru
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. Q.9
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Given that,
S7 = 49
S17 = 289
We know, Sum of n terms;
Sn = n/2 [2a + (n – 1)d]
Therefore,
S7= 7/2 [2a +(n -1)d]
S7 = 7/2 [2a + (7 -1)d]
49 = 7/2 [2a + 6d]
7 = (a+3d)
a + 3d = 7 …………………………………. (i)
In the same way,
S17 = 17/2 [2a+(17-1)d]
289 = 17/2 (2a +16d)
17 = (a+8d)
a +8d = 17 ………………………………. (ii)
Subtracting equation (i) from equation (ii),
5d = 10
d = 2
From equation (i), we can write it as;
a+3(2) = 7
a+ 6 = 7
a = 1
Hence,
Sn = n/2[2a+(n-1)d]
= n/2[2(1)+(n – 1)×2]
= n/2(2+2n-2)
= n/2(2n)
= n2