math terms

Let a = First term, r = common ratio, n = number of terms. Multiply both sides of (i) by r, the common ratio. Subtracting (ii) from (i), we get ..

Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..

1, 3, 5, 7..... (adding 2 to every term) 1, 4, 16, 64 (Multiplying by 4 every term) 20, 17, 14 . (add -3 to every term) The different numbers in a sequence are called terms of sequence. The subscripts denote the position of the term. In the..

Each one of the following series form an A.P. i) 1, 3, 5, 7, ii) 3, 7, 11, 15, iii) 15, 12, 9, iv) x, x - d, x - 2d, ..... The common difference is found by subtracting any term of the series from the immediate succeeding term. In the above example, common difference in th..

2, 5, 8, 11, 14 , 32 37, 33 , 1 A sequence is called infinite if the number of terms is infinite. An infinite sequence has no last term. In this sequence, every term is followed by a new term..

Indicated sum of the terms in a sequence is called a series. The result of performing the additions is the sum of the series...

The series of terms a, ar, ar 2 , ar 3 ,.... in which each term bears a constant ratio to the preceeding term is a geometric progression. The constant ratio is called the common rati..

Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we get ..

) A sequence may be described by giving a formula for its n t h term. (iii) A sequence may be described by specifying its first few terms and a formula to determine the other terms of the sequence in terms of its proceeding terms. A sequence is said..

From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..