Question

Determine the AP whose 4th term is 23 and 8th term is 11​

Answer 1

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Answer 2

• An AP is given as,

$a,a + d,a + 2d$

where a is the first term and d is the common difference

• n term of an AP is defined as,

$t_{n} = a + (n - 1)d$

• Given,

$t_{4} = 23 \\ t_{8} = 11$

• Therefore

$a + 3d = 23 \\ a + 7d = 11$

Subtracting equations we get,

$- 4d = 12 \\ d = - 3$

• Substituting into the equations we get,

$a + 3( - 3) = 23 \\ a - 9 = 23 \\ a = 32$

• So the AP is

$a,a + d,a + 2d \\ 32,29,26,23,......$