What is the sum of numbers lying between 107 and 253, which are divisi

1.	What is the sum of numbers lying between 107 and 253, which are divisible by 5?(a) 5250 (b) 5210 (c) 5220 (d) 5000
Answer» Answer : (c) 5220 The numbers between 107 and 253 divisible by 5 are 110, 115, 120, .......... , 245, 250. This is an A.P with first term (a) = 110 and common difference (d) = 5. Let the last term be the nth term. ∴ T_n = a + (n – 1)d ⇒ 110 + (n – 1) × 5 = 250 ⇒ 5n = 250 – 105 = 145 ⇒ n = 29. ∴ Required sum = \(\frac{n}{2}\) (a + T_n) = \(\frac{29}{2}\)(110 + 250) = \(\frac{29}{2}\) × 360 = 5220

What is the sum of numbers lying between 107 and 253, which are divisible by 5?(a) 5250 (b) 5210 (c) 5220 (d) 5000

Answer»

Answer : (c) 5220

The numbers between 107 and 253 divisible by 5 are

110, 115, 120, .......... , 245, 250.

This is an A.P with first term (a) = 110 and common difference (d) = 5.

Let the last term be the nth term.

∴ T_n = a + (n – 1)d

⇒ 110 + (n – 1) × 5 = 250

⇒ 5n = 250 – 105 = 145

⇒ n = 29.

∴ Required sum = \(\frac{n}{2}\) (a + T_n) = \(\frac{29}{2}\)(110 + 250)

= \(\frac{29}{2}\) × 360 = 5220