Question

find three terms of an ap in which the sum of first two terms is 10 and the sum of last two terms is 16​

Answer 1

Answer:

the sequence is 7/2 , 13/2 , 19/2

Step-by-step explanation:

Given the Sum of first term and second term is 10 and the sum of Second term and third term is 16

Let the sequence be x , x + d , x + 2d

Sum of first term and second term is 10

→ x + x + d = 10

→ 2x + d = 10 -----(1)

Sum of Second term and third term is 16

→ x + d + x + 2d = 16

→  2x + 3d = 16-----(2)

Solve equation no: (1) & (2)

We get d = 3

Substitute 'd' in (1) or (2) we get,

2x + d = 10

2x + 3 = 10

2x = 7

x₁ = ⁷/₂

Thus the sequence is

x₁ = ⁷/₂

x₂ = ⁷/₂ + 3 = ¹³/₂

x₃ = ¹³/₂ + 3 = ¹⁹/₂