JEE MainMathematicsModerateSequences and Series

If 11 A.M.s are inserted between 28 and 10, then find the number
of integral A.M's.

Show answer and solution

Since

A_{1},A_{2},A_{3},\ldots\ldots,A_{11}\ be\ 11

A.M.s
between 28 and 10.
∴

28,A_{1},A_{2},\ldots\ldots\ldots,A_{11},10\ are\ in\ A.P.\

be the common difference of A.P.
Also the number of terms =13

10 = T_{13} = T_{1} + 12d = 28 + 12d

\therefore d = \frac{10 - 28}{12} = - \frac{18}{12} = - \frac{3}{2}

Number of integral A.M's is

Source: Grass-G / M-28 Mathematics Paper FST 16 Jan.docx

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