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In an AP, a_{3} =15 S_{10} =125 Find (d a_{10})^2

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In an AP, $a_{3} = 15$ $S_{10} = 125$
Find $(d \times a_{10})^{2}$

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Theodore Discussed

In an AP,

a_{3} = 15

S_{10} = 125

Find

(d \times a_{10})^{2}

6 mins ago

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6 mins ago

Text solutionVerified

a_{3} = 15,

a + 2 d = 15.

S_{10} = 125

S_{10} =

\frac{10}{2} [2 a + 9 d] = 125 2 a + 9 d = 25 a + \frac{9}{2} d = \frac{25}{2}

a + \frac{9 d}{2} = \frac{25}{2} a + 2 d = 15

\frac{5 d}{2} = - \frac{5}{2} d = - 1, a = 17.

a_{10} = a + 9 d = 17 - 9 = 8

(d \times a_{10})^{2} = (- 1 \times 8)^{2} = 64

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