Question

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

Answer 1

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Answer 2

Answer:

d = -1

a10 = -12

Step-by-step explanation:

Given - a3 = 15 and s10 = 125

wkt a n = a + (n-1) d

therefore , a3 = a + (3-1)d

                  15 = a+2d   - equation 1

wkt S n =  n/2(2a + (n-1)d)

therefore , s10 = 10/2(2a + (10-1)d)

                  125 = 5(2a + 9d)

                   25 = 2a + 9d     - equation 2

multiplying equation 1 by 2,

30 = 2a + 4d     - equation 3

by subtracting equation 3 from equation 2,

  2a + 9d = 25

  -2a - 4d = -30

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         5d = -5

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5d = -5

=> d = -5/5

       = -1

by substituting d value in equation 1,

15 = a + 2(-1)

15 = a -2

a = 15 + 2

a = 17

therefore a10 = a+9d

                       = 17 + 9(-1)

                       = 17 - 9

                       = 12