Questions For Practise(Sequence, Series)
# Short Answer Questions
1)Find the 5th term of the sequence 3,-6, 12,-24,…
2) Find the 7th term of the series 3,6,12,24,…….
3) Find the arithmetic mean and geometric mean
between the two numbers 6 and 54.
4) If the first term of a geometric series is 4 and the sum of first two term is 36, find the common
ratio.
5) How many terms are there in the series ?
In a GP, the first term is 7 and the last term is
448 and sum 889, find the common ratio.
6) Find the 8th term of the series 5,-10,-15, 20 …
7) If the 2nd and 4th term of a GP are -10 and 20
respectively then find first term, common ratio
and 12th term.
8) If 2nd term and 5th term of a GP are 4 and 32
respectively. Find 8th term.
9) 0In a GP if the common ratio is 2 and the 8th
term is 384, find the first term
Which term of the series is 192 ?
10) Find the sum of the following series:
a. 7 terms
b. 8 terms
c. 10terms
8-12+18-……..
11) How many terms of the series 32+48+72+….. will add up to 665 ?
12) Evaluate the following
In a GP if S₆ = 28 and S₃ = 1, find a and r.
13) The first three terms of a G.P. are 2x, 2x+3 & 2x+9. Find x & the value of 5th term.
14) If 4th term of a G.P. is 54 and 6th term is 24,
which term is 7 ?
# Long Answer Questions
1) If the second and fifth term of a GS is 4 and 32, find the series.
2) Given series is 9+3+1+………..+ ¹/₂₄₃.
How many terms are there in the series ?
Calculate the sum.
3) For two unequal numbers show that AM> GM
4)If the AM and GM between two positive and
unequal numbers are 5 and 4 respectively, what
are the numbers ?
or, Find two numbers whose arithmetic mean is 5 and geometric mean is 4.
5) If the AM and GM between two positive and
unequal numbers are 13 and 5 respectively,
what are the numbers ?
6) If the AM and GM between two positive and
unequal numbers are and 6 respectively, what
are the numbers ?
7) The sum of first four terms is 40 and the sum of first two terms is 4 of a geometric series whose common ratio is positive, find the sum of first eight terms.
8) If the AM of two unequal positive real numbers a and b (a>b) be twice as great as their GM, show that:
9) Anisha borrows Rs 4368 which she promises to pay in 6 annual instilments, each installment
being treble of the preceding one. Find the first
and the last installment.
10) The product of three numbers in a GP is 216 and the sum of products of the numbers taken in
pairs is 156. Find the numbers.
11) x + 6, x and x - 3 are the first three terms of a
geometric series. Find the value of x and its fifth
term.
12) If x, 6, y, 24, p are in GS, find the values of x, y,
p given that common ratio is +ve.
13) If 4th term of a G.P. is 54 and 6th term is 24,
which term is 7 ?
14) Insert 3 geometric means between ¹/₃ and 9.
15) Insert 4 GM between ¹/₁₆ and 16; also find the sum of the series.
16) Insert 2 GM between 6 and 48.
17) Insert 3 GM between 5 and 3125.
18) The 2nd term of a GP is 6 and its 5th term is
162. Find the sum of first 5 terms.
19) If 5, a, b, 135 are in GP, find a and b.
20) If 2, m, n, s, are in GP, find m, n and s.
21) The sum of 3 consecutive terms of G.P. is 28 and their product is 512. Find the terms
22) The sum of three terms in AP is 30. If 5 is added to the third term it becomes a GP. Find the
terms.
23) Find two numbers whose AM is 34 & GM is 16. If a, b, c are in AP and x, y, z are in G.P. prove
that. :
24) In a G.P. tp = a, tq = b & tr = c. Then show that a^(q-r) b^(r-p) c^(p-q) = 1.
# Formulas
1. Sum of 1st n natural numbers Sn = 1+2+3+
……. to n terms = ⁿ⁽ⁿ⁺¹⁾/₂
2. Sum of 1st n even numbers Sn = 1 + 2 + 4 +
to n terms = n(n+1)
3. Sum of 1st n odd numbers Sn = 1 + 3 + 5 +
…… to n terms = n²
4. Sum of square 1st n natural numbers Sn=
1² + 2² + 3² +…………to n terms = ⁿ⁽ⁿ⁺¹⁾⁽²ⁿ⁺¹⁾/₆
5. Sum of cubes of 1st n natural numbers Sn =
1³ + 2³ + 3³ +………to n terms= [ⁿ⁽ⁿ⁺¹⁾/₂]²
6. Σn= ⁿ⁽ⁿ⁺¹⁾/₂
7. Σn² = ⁿ⁽ⁿ⁺¹⁾⁽²ⁿ⁺¹⁾/₆
8. Σn³ = [ⁿ⁽ⁿ⁺¹⁾/₂]²
# Rules to find General term
To find general terms we use following rules:
1) If the series/sequence is AS then tₙ=a+(n-1)d
2) If the series/sequence is GS then tₙ = arⁿ-1
3) If the series/sequence is not both AS and GS
we find a pattern.
4) If we cannot use all these methods
mentioned above then tₙ = an² + bn + c.
#Exercise
1) Find the sum of first 5 natural numbers.
2) Find the sum of first 10 even numbers.
3) What is the sum of first 7 odd numbers?
4) Calculate the sum of square of first three natural numbers?
5) Find the sum of cubes of first 5 natural numbers.
# Important Questions for SLC Examination
1) Find the sum of the following series
a. 1 + 3 + 5 + ………….. 25 terms
b. 2 + 4 + 6 + ……….. 21 terms
c. 1 + 2 + 3 + …………. 25 terms
d. 2 + 4 + 6 + ……… 30 terms
e. 1 + 3 + 5 + ………… 50 terms
2) Find the sum of the following series
a. 13 + 23 + 33 …………… +103
b. 13 + 23 + 33 + …………… 8 terms
c. 12 + 22 + 32 + …………….. + 102
d. 12 + 22 + 32 + ……….. 12 terms
3) Find the nth term and sum of n terms of
following series.
a. 2² + 4² + 6² + ……………… n terms
b. (1×2) + (2×3) + (3×4) + ……….. n terms
c. (2×4) + (3×5) + (4×6) + ………….. n terms