Question

Find the 10th common term between the arithmetic series 3+7+11+15+... and 1+6+11 +16+....

Answer 1

Clearly, the first common term in the two series is 11.

LCM of the common differences of the two series = LCM (4, 5) = 20.

Let us now consider an AP in which a =11 and d = 20.

Every term of this AP is a common term of the two given series.

So, the required 10th common term

= {11 + (10 - 1) $\times$ 20} = (11 + 180) = 191.

Hence, 191 is the 10th common term of the two given series.