Question

Sum of first hundred numbers common to the two AP s 12,15,18.... And17, 21,25 is

Answer 1

Answer:

60450

Explanation:

Given,

First A.P.: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, ...

Second A.P.: 17, 21, 25, 29, 33, 37, 41, 45, ...

We have to find the sum of the first 100 numbers common to the two A.P.'s. and we form the A.P. of common terms:

21, 33, 45, ...

First term, a = 21

Common difference, d = 12

Number of terms, n = 100

i.e., the sum of the first 100 terms is

= n/2 * [ a + (n - 1) d ]

= 100/2 * [ 21 + (100 - 1) * 12 ]

= 50 * [ 21 + 99 * 12 ]

= 50 * [ 21 + 1188 ]

= 50 * 1209

= 60450.