An infinite geometric series P has first term and common ratio

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

An infinite geometric series P has first term

10

and common ratio

0.3

. Another infinite geometric series Q has first term

k

and common ratio

0.5

. If the sums of the two series are equal, then

k

equals (a)

10

(b)

\dfrac{50}{13}

(c)

\dfrac{50}{7}

(d)

\dfrac{100}{7}