ARITHMETIC PROGRESSION AND GEOMETRIC PROGRESSION

1.       For each sequence, find the next four terms.

                        i.      2, 4, 6, 8 …

                       ii.      1, 4, 9, 16 …

2.       Find the first five terms of the following sequences whose nth terms are given.

                        i.      t_n = 3n – 2

                       ii.      t_n = n² + n + 1

3.       Find the first three terms of the sequences for which S_n is given.

                        i.      S_n =

                       ii.     

4.       Which of the following list of number are Arithmetic Progressions? Why?

                        i.      1, 3, 6, 10 …

                       ii.      3, 5, 7, 9, 11………

5.       Write the first five terms of the A.P. given the first term a and the common difference d:

                        i.     

                       ii.     

6.       How many terms are there in the A.P. 87, 94, 101, 108, ……… , 339?

7.       Find the common difference and the 11^th terms of the A.P. if a = 100, and t₂₀ = 176

8.       How many three digit natural numbers are divisible by 8.

9.       How many three digit natural numbers are divisible by 6?

10.    Find the sum of all natural numbers between 50 and 250 which are exactly divisible by 3.

11.    Find the sum of all even natural numbers from 1 to 150.

12.    Find three consecutive terms in an A.P. whose sum is 45 and their product is 3240,

13.    Find three consecutive terms in an A.P. whose sum is 12 and the sum of whose squares is 56.

14.    Find five consecutive terms in an A.P. such that the sum of the first three terms is 6 and the sum of the remaining two terms is 14.

15.    A manufacturer produced 650 items in the fourth year and 850 items in the eight year. The items produced increase by a fixed number every year. Find the items produced in the first year.

16.    Find the ninth term of the G.P. 3, 6, 12, 24 …

17.    Write down the first five terms of the geometric progression which has first term 1 and common ratio 4.

18.    Find the 4^th and the 9^th terms of the G.P. with first term 4 and common ratio 2.

19.    Find the common ratio and the 7^th terms of the G.P. 2, -6, 18 …

20.    Find the 69^th terms of the G.P. 1, -1, 1, -1 …

21.    Find the 15^th term of the G.P. 3, 12, 48, 192 …

22.    Find the sum of the G.P. 2, 6, 18 …

23.    If the n^th, (2n)^th, (3n)^th terms of the G.P. are a, b, c respectively then show that

24.    Find three number in G.P. such that the sum of the first two is 8 and their product is 216.

Find three numbers in G.P. such that the sum of the 2^nd and the 3^rd is 30 and their product is 1728.