find the number of terms of an a.p. whose sum is 40 and first and fifth terms are 14 and 2

Step 1: The factor pairs of the last term are (7,2), (14,1), (-1,-14). Step 2: The pair of factors whose sum is equal to -15, the co- efficient of the middle term is (-1,-14). Step 3: Rewrite the expression u..

(iii) If 'a' and 'd' be the first term and common difference of the A.P. {T n }, then the sum of first n terms, S n is given by The form (a) is used when common difference 'd' is known and the form (b) is used when the last term ..

The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from..

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 ..

Question: For the given sequence, suggest possible next three terms and find the general term. -3, 1, 5,---- Answer: First term = -3, Common difference = 1-(-3) = 4 = 5 - 1 Next three terms..

Factorisation of trinomials of the form x 2 +bx+c Trinomials are expressions with three terms. For example, x 2 + 14x + 49 is a trinomial. There is no single method by which all trinomials can be factorised. We need to study the pattern in trinomials and cho..

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 d..

The Greek letter S (read as sigma) denotes the sum. When written before the n t h term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3..

Find the product (ac), of the coefficient of x 2 and the last term. List the factor pairs of ac. Choose a factor pair whose sum is the coefficient of the middle term. Rewrite the polynomial by splitting the middle term. Regroup and..

Question: Find the first five terms of the sequence defined by t n = 6 - 4n. Which term of the sequence is -50? Answer: t n = 6 - 4n When n = 1, t 1 = 6 - 4(1) = 2 When n = 2, t 2 = 6 - 4(..