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OPTIONAL MATHS QUESTION SLC

# Short Answer Questions
Find the 5th term of the sequence 3,-6, 12,-24, …
Find the 7th term of the series 3,6,12,24,…….
Find the arithmetic mean and geometric mean between the two numbers 6 and 54.
If the first term of a geometric series is 4 and the sum of first two term is 36, find the common ratio.
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.
Find the 8th term of the series 5,-10,-15, 20 …
If the 2nd and 4th term of a GP are -10 and 20 respectively then find first term, common ratio and 12th term.
If 2nd term and 5th term of a GP are 4 and 32 respectively. Find 8th term
In a GP if the common ratio is 2 and the 8th term is 384, find the first term
Which term of the series   is  ?
Find the sum of the following series:
  +1+4+…… 7 terms
 8 terms
 10terms
8-12+18-…….. 
How many terms of the series 32+48+72+….. will add up to 665 ?
Evaluate the following
In a GP if S6 = 28 and S3 = 1, find a and r.
The first three terms of a G.P. are 2x, 2x + 3 & 2x + 9. Find x & the value of 5th term.
If 4th term of a G.P. is 54 and 6th term is 24, which term is 7 ?
# Long Answer Questions

If the second and fifth term of a GS is 4 and 32, find the series.
Given series is 9+3+1+………..+ .
How many terms are there in the series ?
Calculate the sum
For two unequal numbers show that AM> GM
If the AM and GM between two positive and unequal numbers are 5 and 4 respectively, what are the numbers ?
Find two numbers whose arithmetic mean is 5 and geometric mean is 4.
If the AM and GM between two positive and unequal numbers are 13 and 5 respectively, what are the numbers ?
If the AM and GM between two positive and unequal numbers are   and 6 respectively, what are the numbers ?
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.
If the AM of two unequal positive real numbers a and b (a>b) be twice as great as their GM, show that 
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.
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.
x + 6, x and x - 3 are the first three terms of a geometric series. Find the value of x and its fifth term.
If x, 6, y, 24, P are in GS, find the values of x, y, p given that common ratio is +ve.
If 4th term of a G.P. is 54 and 6th term is 24, which term is 7 ?
Insert 3 geometric means between  and 9.
Insert 4 GM between and 16; also find the sum of the series.
Insert 2 GM between 6 and 48.
Insert 3 GM between 5 and 3125.
The 2nd term of a GP is 6 and its 5th term is 162. Find the sum of 1st 5 terms.
If ,x,y,z are in G.P., find the values of x, y & z.
If 5, a, b, 135 are in GP, find a and b.
If 2, m, n, s,  are in GP, find m, n and s.
The sum of 3 consecutive terms of G.P. is 28 and their product is 512. Find the terms
The sum of three terms in AP is 30. If 5 is added to the third term it becomes a GP. Find the terms.
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.
In a G.P. tp = a, tq = b & tr = c. Then show that aq-r br-p cp-q = 1.
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