Question

Third term of an AP is 34.sixth term of an AP is 67
1 write the AP
2 What is 50th term
3 Is 327 will be a term

Answer 1

Solution :

3rd term of an A.P. = 34

6th term of an A.P. = 67

★ General terms of an A.P.

⇒ Tₙ = a + (n - 1)d.

⇒ T₃ = 34.

⇒ T₃ = a + (3 - 1)d.

⇒ T₃ = a + 2d.

⇒ a + 2d = 34. ⇒ (1).

⇒ T₆ = 67.

⇒ T₆ = a + (6 - 1)d.

⇒ T₆ = a + 5d.

⇒ a + 5d = 67. ⇒ (2).

From equation (1) & (2), we get.

⇒ a + 2d = 34.

⇒ a + 5d = 67.

We get,

⇒ - 3d = - 33.

⇒ d = 11.

Put the value of d = 11 in equation (1), we get.

⇒ a + 2d = 34.

⇒ a + 2(11) = 34.

⇒ a = 34 - 22.

⇒ a = 12.

First term = a = 12.

Common difference = d = 11

Answer 2

✯Solution :

☞calculation of d :

• T3 = a+2d = 34
• T6 = a+5d = 67
• (a+5d)-(a+2d) = 67-34
• 3d = 33
• d = 11

☞ calculation of a :

• T3 = a+2d
• 34 = a+2(11)
• a = 34-22
• a = 12

☞ 50th term is ,

• T50 = a +49d
• 12 + 49(11)
• 12+539
• 551

☞327 is a term ??

• Tn = a+(n-1)d
• 327 = 12+(n-1)11
• 315 = 11n-11
• n = 315+11/11
• n = 29.63
• this is not a term of this series

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