Find the sum to n terms of the series whose nth term is given by n (n + 1) (n + 4).
an = n (n + 1) (n + 4) = n(n2 + 5n + 4) = n3 + 5n2 + 4n
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
Show that the products of the corresponding terms of the sequences a,ar,ar2, ...arn-1 and A, AR, AR2, ,,,ARn-1 form a G.P, and find the common ratio.
Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015 …
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
Find the derivative of 99x at x = l00.
The sum of first three terms of a G.P. is and their product is 1. Find the common ratio and the terms.
A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
Find the sum to n terms in the geometric progression x3, x5, x7 ... (if x ≠ ±1)