Question

number of terms common to the ap 3,7,11,----407and2,9,16,------,709is

Answer 1

For A.P. 1 = 3, 7, 11 ,..... 407.

A. P. 2 = 2, 9, 16..... 709.

An = a + ( n - 1 ) d

407 = 3 + ( n - 1 ) 4

407 - 3 = ( n - 1 ) 4

404 / 4 = ( n - 1 )

n 1 = 101 + 1 = 102.

For A.P 2,

An = a + ( n - 1 ) d

709 = 2 + ( n - 1 ) 7

709 - 2 = ( n - 1 ) 7

707 / 7 = ( n - 1 )

n 2 = 101 + 1 = 102.

⏺️n1 = n2 = 102

✔️ 102 terms are common to the A. P.