Question

The sum of the 5 term of an arithmetic sequence is 250 and the sum of the first 10 term is 750 a)Write the three terms of the sequence?​

Answer 1

Answer:

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Step-by-step explanation:

given we have,

S₅ = 250

S₁₀ = 750

we have to find a₁ a₂ and a₃

so,

Sn = n/2 (2a + (n-1)d)

S₅ = 5/2 (2a + (5-1)d)

250 = 5/2 (2a + 4d)

250 * 2 / 5 = 2a + 4d

500 / 5 = 2a + 4d

2a + 4d = 100 ------(1)

S₁₀ = 10/2 ( 2a + (10-1)d)

750 = 5 ( 2a + 9d)

750 / 5 = 2a + 9d

2a + 9d = 150 -----(2)

by elimination method from (1) and (2),

(2a - 2a) + (4d - 9d) = 100 - 150

-5d = -50

5d = 50

d = 50/5

d = 10

2a + 4d = 100

2a + 4(10) = 100

2a + 40 = 100

2a = 100 - 40

2a = 60

a = 60/2

a = 30

therefore,

a₁ = a = 30

a₂ = a₁ + d = 30 + 10 = 40

a₃ = a₂ + d = 40 + 10 = 50