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In an AP : Given a_{3}=15, S_{10}=125 find d and a_{10}

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In an AP :
Given $a_{3} = 15, S_{10} = 125$ find $d$ and $a_{10}$

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In an AP :
Given

a_{3} = 15, S_{10} = 125

find

d

and

a_{10}

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

a_{3} = 15

Let the first term

= a

Common difference

= d

∴ a_{3} = a + 2 d = 15 ⟶ (1)

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

2 a + 9 d = 25 ⟶ (2)

multiplying

(1)

2

and then subtracting with

(2)

2 a + 4 d = 30

2 a + 9 d = 25

- - -

\overline{- 5 d = 5}

\Rightarrow d = - 1

putting

d

in equation

(1)

\Rightarrow a + (- 1) 2 = 15

\Rightarrow a = 17

\Rightarrow a_{10} = a + 9 d = 17 - 7 = 8

Hence, the answer is

- 1, 8.

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