Question

If the sum of first 7 terms of AP is 49 and that of first 17 terms is 289 then find the sum of first n terms

Answer 1

Given that,

S7 = 49

S17 = 289

S7

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

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

Answer 2

Refers to attachment ♡♡~