Question

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​

Answer 1

Answer:

Step-by-step  explanation:

Given that sum of first 7 terms is 49 and sum of first 17 terms is 289

To find- Sum of first n terms

Solution-

n/2(2a + 6d) = 49                  

n/2(2a + 16d) = 289              

S7 = 7/2 [2a + (7 - 1)d]

49 = 7/2 [2a + 16d]

7 = (a + 3d)

a + 3d = 7 ... (i)

Similarly,

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),

a + 3(2) = 7

a + 6 = 7

a = 1

Sn = n/2 [2a + (n - 1)d]

= n/2 [2(1) + (n - 1) × 2]

= n/2 (2 + 2n - 2)

= n/2 (2n)

= n²

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