Question

10 th term of an arithmetic sequence is 30 and 30 tem is 10 find the common difference

Answer 1

Given : 10th term of an arithmetic progression is 30 and it's 30th term is 10

To find : It's common difference

Solution :

An arithmetic progression is a sequence of numbers in which common difference between two consecutive terms is always constant.

nth term of an AP is given by,

• an = a + ( n - 1 )d

Here,

• an = nth term
• a = First term
• d = Common difference
• n = Number of terms

So 10th term of an AP is given by,

⇒ an = a + ( n - 1 ) d

⇒ 30 = a + ( 10 - 1 ) d

⇒ 30 = a + 9d ---( Eqn 1 )

30th term of an AP is given by,

⇒ an = a + ( n - 1 ) d

⇒ 10 = a + ( 30 - 1 ) d

⇒ 10 = a + 29d ---( Eqn 2 )

Subtract equation 1 from equation 2 to eliminate a variable a.

⇒ 10 - 30 = a + 29d - ( a + 9d )

⇒ - 20 = a + 29d - a - 9d

⇒ - 20 = 20 d

⇒ - 1 = d

Hence the common difference of AP is - 1.