Question

if the sum of first 8 and 19 terms are 64 and 361 respectively.find the (1) common difference (2)sum of n terms of the series

Answer 1

bta rha hu ki nhi maloom h phir bhi nhi suntye

Answer 2

Answer:

• Sum of n terms in AP :

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

───────────────

⇒ S₈ = 64

⇒ 8/2 × (2a + 7d) = 64

⇒ 4 × (2a + 7d) = 64

⇒ 2a + 7d = 16 — eq. ( I )

⇒ S₁₉ = 361

⇒ 19/2 × (2a + 18d) = 361

⇒ 19 × (a + 9d) = 361

⇒ a + 9d = 19 — eq. ( II )

• Multiplying eq.( II ) by 2 & Subtracting from eq.( I ) from eq.( II ) :

↠ 2a + 18d - 2a - 7d = 38 - 16

↠ 11d = 22

↠ d = 2

• Substitute d value in eq. ( II ) :

⇒ a + 18 = 19

⇒ a = 19 - 18

⇒ a = 1

━━━━━━━━━━━━━━━━━━━━━━━━

⋆ Sum of nth terms of the AP :

↠ 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 = n × n

↠ Sn = n²

∴ Sum of nth terms of the AP is n².