Find the number of common terms in the following sequences (each of which is an A.P) which are less than $10, 000$ .
$S_{1} : 37, 103, 169, \dots$
$S_{2} : 17, 82, 147, \dots$

5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $2$
$37 + 66 a = 17 + 65 b$
$20 + 66 a = 65 b$
$b = \frac{20 + 66 a}{65} = \frac{65 a}{65} + \frac{a + 20}{65}$
For $a = 45$ , we will get the first term common
$37 + 66 \times 45 = 3007$
LCM of $65, 66$ is $4290$
So the next term is $7297$
Hence number of common terms will be $2$

Suggest Corrections

Similar questions

Show that each of the following sequences is an A.P. Also, find the common difference and write 3 more terms in each case.

(i) $3, - 1, - 5, - 9 \dots \dots$

(ii) $- 1, \frac{1}{4}, \frac{3}{2}, \frac{11}{4}, \dots \dots$

(iii) $\sqrt{2}, 3 \sqrt{2}, 5 \sqrt{2}, 7 \sqrt{2}, \dots \dots$

(iv) $9, 7, 5, 3, \dots \dots$

\sqrt{2}, 3 \sqrt{2}, 5 \sqrt{2}, 7 \sqrt{2}, . . .

S_{1}

S_{2}

n

S_{1} / S_{2} = λ

\frac{2}{3}, \frac{4}{5}, \frac{6}{7}, . . . .

S_{1}, S_{2}, S_{3}

S_{1} + S_{3} = 2 S_{2}

Join BYJU'S Learning Program