The number of the common terms in the two sequences 17, 21, 25, . . . . . 817 and 16, 21, 26 . . .. 851 is
Explanation
Calculation:
17, 21, 25, . . . . . 817
Common difference of first sequence = d1 = 21 - 17 = 4
16, 21, 26 . . .. 851
Common difference of second sequence = d = 21 - 16 = 5
Now, LCM of d1 and d2 = 4 × 5 = 20
So, common differnce = d = 20
First common term in both the sequences is 21.
∴ a = 21
New sequence: a, a + d, a + 2d, ...
or 21, 41, 61, 81, ... 801
As we know, nth term = a + (n - 1) d
⇒ 801 = 21 + (n - 1) × 20
⇒ (n - 1) × 20 = 780
⇒ (n - 1) = 39
∴ n = 40
The total number of terms common in both the sequences is 40.
Explanation
Calculation:
17, 21, 25, . . . . . 817
Common difference of first sequence = d1 = 21 - 17 = 4
16, 21, 26 . . .. 851
Common difference of second sequence = d = 21 - 16 = 5
Now, LCM of d1 and d2 = 4 × 5 = 20
So, common differnce = d = 20
First common term in both the sequences is 21.
∴ a = 21
New sequence: a, a + d, a + 2d, ...
or 21, 41, 61, 81, ... 801
As we know, nth term = a + (n - 1) d
⇒ 801 = 21 + (n - 1) × 20
⇒ (n - 1) × 20 = 780
⇒ (n - 1) = 39
∴ n = 40
The total number of terms common in both the sequences is 40.
