Question

If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.

Answer 1

Seventh terms of AP

a₇ = a + (7 - 1) d

a₇ = a + 6d

seven times seventh term 

= 7 (a + 6d)

= 7a + 4 d

fifth term of AP

a₅ = a + (5 - 1)d

a₅ = a + 42 d

five times fifth term

= 5(a + 4d)

= 5a + 20 d

According to question

7a + 42 d

∴ 5a + 20 d

2a = 22 d

a = -11 d...(1)

12^th term of AP

a₁₂ = a + 11 d

putting the value of equation (1)

a₁₂ = -11 d + 11d

a₁₂ = 0

Hence the twelth term of AP is 0

According to question 

7a + 42 d = 5a + 20 d

2a = -22 d

a = -11 d...(1)

12_th term of AP

a₁₂ = a + 11 d

Putting the value of equation (1)

a₁₂ = -11 d + 11 d

a₁₂ = 0

Hence the twelth term of AP is a