Question

please answer the 4th question

Answer 1

Answer- The above question is from the chapter 'Arithmetic Progressions'.  

Concept used: 1) Common difference (d) = a₂ - a₁  

2) aₙ = a + (n - 1)d

where aₙ = nth term or last term of an AP

a = first term of AP

n = Number of terms of AP

d = Common difference  

Given question: Find the common difference of an A.P. in which a₂₅ - a₁₂ = - 52.  

Solution: We know that aₙ = a + (n - 1)d.

Put n = 25, we get,

a₂₅ = a + (25 - 1)d

a₂₅ = a + 24d --- (1)  

Put n = 12, we get,

a₁₂ = a + (12 - 1)d

a₁₂ = a + 11d --- (2)  

It is given that a₂₅ - a₁₂ = - 52.

Substituting the values from (1) and (2), we get,

a + 24d - (a + 11d) = - 52

a + 24d - a - 11d = - 52

13d = - 52

d = - 52 ÷ 13

d = - 4  

∴ The common difference of an A.P. in which a₂₅ - a₁₂ = - 52 is - 4.