Sequence & Series Level-3 Quiz-1

1. Consider the two sequences, 3, 6, 9, 12, 15, … 102 and 4,
8, 12, 16, … 124. Find the number of terms common to
both the sequences

2. The fourth term of an A.P. is 24 and the 44th term is 124.
Find t 24.

3. In a geometric progression, the first three terms are 10a
+ 36, 6a + 12 and 4a, respectively. Find the sixth term of
the geometric progression, if a > 0.

4. If 5x + y, 3x + 2y and 3x + y are in arithmetic progression
and 5x + 1, 3(x + 1) and 3x are in geometric progression,
fi nd (x, y).

5. Find the series in geometric progression for which the
sum to infinity is 1 and |r| < 1.

6. In an arithmetic progression, the sum of the squares
of the seventh term and the eleventh term is 482. The
product of its second term and the sixteenth term is 29.
Find the product of its fi rst and the seventeenth terms

7. The fi rst term of an arithmetic progression consisting of
integers, is the common ratio of a geometric progression.
The fi rst term of the geometric progression is the
common difference of the arithmetic progression. The
sum of the fi rst 11 terms of the arithmetic progression is
341 and the sum of the fi rst three terms of the geometric
progression is 18. Find the sum of the common difference
and the common ratio.

8. In an arithmetic progression, the 10th term is 11 and the
11th term is 10. How many consecutive terms (starting
from the fi rst term) of the arithmetic progression should
be considered so as to make their sum equal to zero?

9. Two new charity organizations C 1 and C 2 were formed,
with x members each, on January 1, 2003. On the fi rst
day of each subsequent month in C 1 , the number of
members increases by a certain number a, while in C 2 ,
the number of members increases in such a way that
the ratio of the number of members in a month to the
preceding month bear a ratio equal to b. On May 1, 2003,
both organizations had the same number of members. If
a = 20x , fi nd b

10. Find the sum of the fi rst 50 terms of the series
1 − 3 − 5 − 7, 3 − 5 − 7 − 9, 5 − 7 − 9 − 11………..