Question

The sum of the first 7 terms of an AP is 49 and yhe sum of its first 17 terms is 289 . find he sum of its first n term (10th class question)​

Answer 1

Answer - n raised to the power 2

Step-by-step explanation:

Hope this helps u

Answer 2

GIVEn

The sum of the first 7 terms of an AP is 49 and the sum of its first 17 terms is 289 .

TO FINd

find he sum of its first n term

SOLUTIOn

• S₇ = 49
• S₁₇ = 289

→ S₇ = n/2[2a + (n - 1)d]

→ 49 = 7/2[2a + (7 - 1)d]

→ 49 = 7/2[2a +6d]

→ 49 × 2/7 = [2a + 6d]

→ 2a + 6d = 14

→ 2(a + 3d) = 14

→ a + 3d = 7 ---(i)

_____________________

→ S₁₇ = n/2[2a + (n - 1)d]

→289 = 17/2[2a + (17-1)d]

→ 289 × 2/17 = 2a + 16d

→ 2a + 16d = 34

→ 2(a + 8d) = 34

→ a + 8d = 17 ---(ii)

_____________________

Subtract both the equations

→ (a + 3d) - (a + 8d) = 7 - 17

→ a + 3d - a - 8d = -10

→ - 5d = -10

→ d = 10/5 = 2

Putting the value of d in eqⁿ - (i)

→ a + 3d = 7

→ a + 3 × 2 = 7

→ a + 6 = 7

→ a = 7 - 6 = 1

Hence, a = 7 and d = 2

_____________________

Now, the value of sum of " n " 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 × 2n

→ Sn = n²