Find the sum of all odd numbers between 100 and 150.

Question

KnowledgeBoat · Accepted Answer

The odd numbers between 100 and 150 are : 101, 103, 105,........, 149. Let total number of terms in A.P. be n. We know that, ∴ an = a + (n - 1)d Given, a = 101 an = 149 d = 103 - 101 = 2 ⇒ 149 = 101 + (n - 1)2 ⇒ 149 - 101 = (n - 1)2 ⇒ 48 = (n - 1)2 ⇒ = (n - 1) ⇒ 24 = (n - 1) ⇒ n = 24 + 1 ⇒ n = 25. We know that, Sum of n terms of an A.P. is given by, ∴ Sn = (a + l) ⇒ S25 = (101 + 149) = = 25 × 125 = 3125. Hence, S25 = 3125.

Mathematics

Find the sum of all odd numbers between 100 and 150.

AP

Related Questions

Find the sum of all even numbers between 10 and 100.

Find the sum of first fifteen multiples of 8.

The 4th term of an A.P. is 22 and 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series upto 8 terms.

In an Arithmetic Progression (A.P.), the fourth and sixth terms are 8 and 14 respectively. Find the :
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.

Mathematics

Find the sum of all odd numbers between 100 and 150.

AP

Related Questions

Find the sum of all even numbers between 10 and 100.

Find the sum of first fifteen multiples of 8.

The 4th term of an A.P. is 22 and 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series upto 8 terms.

In an Arithmetic Progression (A.P.), the fourth and sixth terms are 8 and 14 respectively. Find the :(i) first term(ii) common difference(iii) sum of the first 20 terms.

In an Arithmetic Progression (A.P.), the fourth and sixth terms are 8 and 14 respectively. Find the :
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.