# Sequences and Series - Online Test

Q1. The next term of the sequence 1, 2, 4, 7,11,…. Is
Explaination / Solution:

here,

where n = 1,2,3,....

so, for 6th term n = 6

Q2. The next term of the sequence, 2, 6, 12, 20, …..is
Explaination / Solution:

nth term of given sequence is n(n+1) so the 5th term is 5(5+1)=30

Q3. The next term of the series  is
Explaination / Solution:

Terms of given sequence can be written as

so the required term is 33/32

Q4. Which term of the sequence 8 – 6i, 7 – 4i, 6 – 2i, ….is a real number ?
Explaination / Solution:

for real n, imaginary part = 0

so 2n - 8=0

which gives, n = 4

Q5. All the terms in A.P., whose first term is a and common difference d are squared. A different series is thus formed. This series is a
Explaination / Solution:

the series obtained will not follow rules of AP, GP and HP

Q6. If a, 4, b are in A.P.; a, 2, b are in G.P.; then a, 1, b are in
Explaination / Solution:

As a,4,b are in AP so, ................(i)

Also a,2,b are in GP so, ab = 4...................(ii)

from (i) and (ii)

hence a, 1 , b are in HP

Q7. The eleventh term of the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, ….. is
Explaination / Solution:

here,

Q8. pth term of an A.P. is q and qth term is p, its (p+ q)th term is
Explaination / Solution:

Q9. The sum of 40 A.M.’s between two number is 120. The sum of 50 A.M.’s between them is equal to
Explaination / Solution:

sum of n number of A.M's between two numbers a and b is given by

so,

therefore sum of 50 A.M's between a and b is,

Q10. In an A.P., sum of first p terms is q and sum of first q terms is p. Sum of its p + q terms is
Explaination / Solution: