Question

In an AP given that a3 = 15 , s10 = 125 , find d and a10

Answer 1

Answer:

d = -1 and a10 = 8

Step-by-step explanation:

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Formula:-

nth term of AP, tn = a + (n-1) d  

Sum of n terms Sn = n/2[2a + (n-1)d]

a - first term and d = common difference

To find a and d

It is given that, a3=15 ,S10=125

We can write a + 2d = 15  ----(1)

10/2[2a + 9d ] = 125

⇒5[2a + 9d ] = 125

⇒2a + 9d = 25  ----(2)

(1)*2 ⇒ 2a + 4d = 30 ---(3)

(2) - (3) ⇒

5d = -5

d = -1

eq (1) ⇒ a + 2d = 15

a + -1*2 = 15

a = 15 + 2 = 17

To find a10

a10 = a + 9d = 17 + 9*-1 = 17 - 9 = 8

Answer 2

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