Determine the Ap whose 4th term is 15 and the difference of 6th term is 16
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Let the A.P. be a, a+d, a+2d,.......
⇒ The third term = a3 = a+2d = 16.........(i)
and seventh term = a7 - a + 6d
Given that a7 - a5 = 12
⇒ (a+6d) - (a+4d) = 12
⇒ a+6d - a - 4d = 12
⇒2d = 12
⇒ d = 6
substituting the value of d = 6 in (i)
a + 12 = 6
a=4
The first term of the A.P. is 4 and the common difference is 6.
∴ The A.P. is 4,10,16,22,28,34,...........
∴ The fifth term = a5 = a + 4d
⇒2d = 12
⇒ d = 6
substituting the value of d = 6 in (i)
a + 12 = 6
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