Find the 2nd term and rth term of an A.P. whose 6th term is 12 and 18th term is 22
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Given:
- ⇒ a₂ = 10
- ⇒ a₆ = a₄ + 12
To find:
- ⇒ A.P
Formula used:
⇒ an = a + (n - 1)d
Now,
⇒ a₂ = 10
⇒ a + d = 10
⇒ a = 10 - d ......(1)
Now, according to question,
⇒ a₆ = a₄ + 12
⇒ a + 5d = a + 3d + 12 ......(2)
Now, put the value of 'a' from Eq (1) in Eq (2). We get,
⇒ 10 - d + 5d = 10 - d + 3d + 12
⇒ 10 + 4d = 22 + 2d
⇒ 10 + 4d - 22 - 2d = 0
⇒ -12 + 2d
⇒ 2d = 12
⇒ d = 12/2
⇒ d = 6
Now, put the value of d in Equation (1), we get
⇒ a = 10 - d
⇒ a = 10 - 6
⇒ a = 4
Hence, A.P is 4, 10 , 22 , 28 , 34
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