Question #6a3be

1 Answer
Mar 22, 2015

#512#

Here are two methods of solution, one algebraic and one arithmetical.

Algebraic

The #k# th term is #ar^(k-1)#,
so #ar^(k-1)=162#.

The sum of the first #k# terms is
#S_k=a(1-r^k)/(1-r)=(a-ar^k)/(1-r)=(a-(ar^(k-1))r)/(1-r)=1562#

Substituting,we get:

#(a-162(3/4))/(1-(3/4))=1562#

Algebra gives us #a=512#

Arithmetical

Work backwards from the #k# th term.

#1/r = 4/3#

The #k-1# th term is #162*4/3=216#.

The sum #216+162 < 1562#, so keep working backwards:

The previous term is #216 * 4/3=288# and the sum is still too small.

Continue until we get: The terms we need are:

#512+384+288+216+162#