Question

The number of the common terms in the two sequences 17, 21, 25, . . . . . 817 and 16, 21, 26 . . .. 851 is
1. 28
2. 39
3. 40
4. 87

Answer 1

Correct Answer - Option 3 : 40

Calculation:

17, 21, 25, . . . . . 817

Common difference of first sequence = d₁ = 21 - 17 = 4

16, 21, 26 . . .. 851

Common difference of second sequence = d2 = 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.