Sequences and series questions | form three Basic Mathematics

Find the first term and the common difference of an arithmetic prograssion whose 5^th term is 21 and 8^th term is 30.

Find the 10^th term of a sequence whose first three consecutive terms are 5, 15 and 45. (Leave the answer in exponent form).

1. Explain with examples the relationship between sequences and series.
2. Show that the sum of the first n natural numbers is given by the formula .
3. By using the formula in (ii) above calculate the sum of the first 100 natural numbers.

Given that 49, x and 81 are consecutive terms of a geometric progression. Find :

1. the value of x
2. the geometric mean.

If an arithmetic progression has A₁ as the first term and d as the common difference,

1. Write the second , thirs , fourth and fifth terms,
2. Establish the formula for the sum of the first five terms of the arithmetic progression by using the results in part (i)

The first and second terms of a geometric progression are 3 and 9 respectively.

1. Find the third , fourth and fifth terms.
2. Verify that the sum of the first 5 terms is given by by using the results in part (i).

If the third term of a geometric progression is 100 and the sixth term is 800, find the fifth term and the sum of the two terms.

The second term of an A.P. is 2 and the sixth term is -14. What is the

1. first term
2. common difference?

The sum of the first two terms of a geometrical progression is 10 and the sum of the first four terms is 40. Given that all terms of the progression are positive show that;

1. the common ratio is
2. the sum of the first n terms is 5(3^n/2-1).

In an arithmetical progression , the thirteenth term is 27, and the seventh term is three times the second term. Determine the sum of the first ten terms.