5. Find the 12th term of a GP. whose 8th term is 192 and the common ratio is 2.
6. The 4th term of a geometric progression is
2
3
and the seventh term is
16
81 .
Find the
geometric series.
7. If the geometric progressions 162, 54, 18 ..... and
2 22
, , ....
81 27 9 have their n
th term
equal. Find the value of n.
OPTIONAL EXERCISE
[For extensive Learning]
1. Which term of the AP : 121, 117, 113, . . ., is the
first negative term?
[Hint : Find n for an
< 0]
2. The sum of the third and the seventh terms of an
AP is 6 and their product is 8. Find the sum of
first sixteen terms of the AP.
3. A ladder has rungs 25 cm apart. The rungs
decrease uniformly in length from 45 cm at the
bottom to 25 cm at the top. If the top and the
bottom rungs are
1
2
2
m apart, what is the length
of the wood required for the rungs?
[Hint : Number of rungs = 250 1
25
+ ]
4. The houses of a row are numbered consecutively
from 1 to 49. Show that there is a value of x such
that the sum of the numbers of the houses preceding
the house numbered x is equal to the sum of the numbers of the houses following it. And
find this value of x.
[Hint : Sx – 1 = S49 – Sx
]
5. A small terrace at a football ground comprises of 15 steps each of which is 50 m long and
built of solid bricks.