Question

If 20th term of an Ap is 1/40 and 40th term of the same Ap is 1/20 , then the sum of 800 terms is :
1: 390.5
2: 400.5
3: 410.5
4: 405.5
​

Answer 1

Step-by-step explanation:

3 is the correct answer

Answer 2

Gɪᴠᴇɴ :-

• 20th term of an AP = (1/40)
• 40th term of same AP = (1/20)

Tᴏ Fɪɴᴅ :-

• sum of 800 terms of that AP ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

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

Sᴏʟᴜᴛɪᴏɴ :-

Given That,

→ T₂₀ = (1/40)

→ T₂₀ = a + (20 - 1)d

→ a + 19d = (1/40) -------------- Eqn.(1)

Also,

→ T₄₀ = (1/20)

→ T₄₀ = a + (40 - 1)d

→ a + 39d = (1/20) -------------- Eqn.(2)

Subtracting Eqn.(1) from (2) Now,

→ (a + 39d) - (a + 19d) = (1/20) - (1/40)

→ a - a + 39d - 19d = (2 - 1)/40

→ 20d = (1/40)

→ d = (1/800)

Putting This value in Eqn.(1) Now,

→ a + (19/800) = (1/40)

→ a = (1/40) - (19/800)

→ a = (20 - 19)/800

→ a = (1/800)

Therefore ,

→ S₈₀₀ = (n/2)[2a + (n - 1)d]

→ S₈₀₀ = (800/2)[ 2 * (1/800) + (800 - 1)(1/800) ]

→ S₈₀₀ = 400 [ (1/400) + (799/800) ]

→ S₈₀₀ = 400 [ (2 + 799)/800 ]

→ S₈₀₀ = 400 * (801/800)

→ S₈₀₀ = (801)/2

→ S₈₀₀ = 400.5 (Option 2). (Ans.)

Hence, sum of 800 terms of AP will be 400.5.