Question

Sum of the first 10 terms is 50 and the sum of the next 10 terms is 250. find the 15th term in ap

Answer 1

hope it helps.........

Answer 2

Hi !

S₁₀ = 50

n/2 [ 2a + (n-1)d ] = 50

10/2 [ 2a + 9d ] = 50

5 [ 2a + 9d ] = 50

2a + 9d = 10                  ---------------> [ 1]

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S₁₀ + S₁₀ = 50 + 250 = 300

S₂₀ = 300

S₂₀ = 20/2 [ 2a + 19d ]

10 [ 2a + 19d  ] = 300

2a + 19d = 30                 -----------> [2]

(2) - (1)

           
  2a + 19d = 30    
- 2a + 9d = 10
=========
 10d = 20

d = 2

2a + 9d = 10

2a + 18 = 10

2a = -8

a = -4

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15th term = a₁₅

a₁₅ = a + 14d
     = -4 + 14 ×2
    = -4 + 28
    = 24