Sequences and Series
The sum of (x+5) observations is (x4−625). Find the mean of the observations.
Show that a1,a2,…,an,…form an AP where anis defined as below : (i) an=3+4n (ii) an=9−5n. Also find the sum of the first 15 terms in each case.
A person has 2 parents, 4 grandparents, 8 great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his one.
In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is 112.
A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.