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

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Mathematics

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

AP

Related Questions

Find the sum of all 2-digit natural numbers divisible by 5.

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

Find the sum of first fifteen multiples of 8.

The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 - n). Find ∶(a) its first term and common difference(b) sum of its first 25 terms

The n^th term of an Arithmetic Progression (A.P.) is given by the relation T_n = 6(7 - n). Find ∶
(a) its first term and common difference
(b) sum of its first 25 terms