If the pth, qth and rth term of a G.P are a, b, c respectively prove that aq-r br-p cp-q = 1
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Find a G.P. for which sum of the first two term is -4 and the fifth term is 4 times thethird term.
Let S be the Sum, P the product and R the sum of reciprocals of n terms in a G.P
Prove that P2 Rn = Sn
The Sum of the first four terms of an A.P. is 56. The Sum of the last four term is112. If its first term is 11, then find the no. of terms.
Find the sum of integers from 1 to 100 that are divisible by 2or5
Find the sum to n terms of the series 5+11+19+29+41 + ----
If A. M. and G. M of two positive no. a and b are 10 and 8 respectively find the no.
Between 1 and 31, m number have been inserted in such a way that the resulting
sequence is an A.P. and the ratio of 7th and (m-1)th no. is 5:9 find the value of m.
The difference between any two consecutive interior angles of a polygon is 50. If
the smallest angle is 1200, find the no. of the sides of the polygon.
If the Sum of n terms of an A.P. is 3n2+n and its mth term is 164, fins the value of m.
The ratio of the sums of m and n terms of an AP is m2:n2. Show that the rates of mth
and nth term is (2m-1) : (2n-1).
If the first and the nth terms of a G.P. are a and b respectively and P is the product
of n terms prove that P2 = (ab)n.
The Sum of first three terms of a G.P. is 16 and the Sum of the next three term is128. determine the first term, the common ratio and the Sum to n terms of the G.P.
Find the sum to n terms of 3×12 + 5 × 22 + 7 ×32 +....
Insert three no. between 1 and 256 so that the resulting sequence is a G.P.
If the Sum of n terms of an A. P is (pn + qn2), where p and q are constants find the
common difference.
If a and b are the roots of x2-3x+p = 0 and c, d are roots of x2 – 12x + 9 = 0 where a,
b, c , d from G.P, prove that (q+p): (q-p) = 17:15
The number of bacteria in a certain culture double every hour. If there were 30
bacteria in the culture originally, how many bacteria will be present at the end of
2nd hour, 4th hour and nth hour.
If a, b, c and d are in G.P show that (a2+b2+c2) (b2+c2+d2) = (ab + bc + cd)2
Find the sum 0.6 + 0.66 + 0.666 + ---
Let the sum of n, 2n, 3n terms of an A. P. be S1, S2 and S3 respectively show that
S3 = 3 (S2 – S1)
Find the sum to n terms of the series 3×8 + 6×11+ 9×14 + - - -
Find the sum of the sequence 7, 77, 777, ------ to n terms
In an A. P. the first term is 2 and the sum of the first five terms is one fourth of next
five terms. Show that 20th term is -112.
In an A. P. is mth term is n and nth term is m, find the pth term.
The Sum of three no. in G.P is 56. If we subtract 1, 7, 21 from these no. in that orderwe obtain an A. P. find the no.
Find the Sum to n terms of n2 + 2n
The sum of first three terms of a G. P is 13/12 and their product is -1. Find thecommon ratio and the terms.
Insert 6 numbers between 3 and 24 such that the resulting sequence is an A. P.
150 workers were engaged to finish a job in a certain no. of days 4 workersdropped out on the second day, 4 more workers dropped out on the third dayand so on. It took 8 more days to finish the work find the no. of days in whichthe work was completed
Fins the of all two digit no. which when divided by 4 yields 1 as remainder
Show that the sum of (m+n)th and (m-n)th terms of an A. P. is equal to twice the
mth term.
Find the sum to n terms of the series 12 + (12 + 22 )+ (12 + 22 + 32 )+ - - - -
The sum of n terms of two A. P are in the ratio (3n+8) : (7n+15). Find the ratioof their 12th terms.
The Fibonacci sequence is defined by
Find
Write the first five terms of the following sequence and obtain the corresponding series:
Find the 20th term in the following sequence whose nth term is
Find the 9th term in the following sequence whose nth term is
Find the 7th term in the following sequence whose nth term is
Find the 17th term in the following sequence whose nth term is
Write the first five terms of the sequences whose nth term is
Write the first five terms of the sequences whose nth term is an = 2n
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