Insert six A.M.s between 15 and -13.

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Solution

Let $A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6}$ be the 6 A.M's between 15 and -13

Then,

$15, A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6}, - 13$ are in A.P. of 8 terms

Here, $- 13 = a_{8} = a + 7 d$

$\Rightarrow - 13 = 15 + 7 d$

Or d = -4 ..... (i)

$∴ A_{1} = a + d = 15 - 4 = 11$

$A_{2} = a + 2 d = 15 - 2 (4) = 7$

$A_{3} = a + 3 d = 15 - 4 (3) = 3$

$A_{4} = a + 4 d = 15 - 4 (4) = - 1$

$A_{5} = a + 5 d = 15 - 4 (5) = - 5$

$A_{6} = a + 6 d = 15 - 4 (6) = - 9$

The 6 A.M.s between 15 and -13 are 11, 7, 3, -1, -5 and -9.

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