Question

Solution

Let a, b be roots of required quadratic equation

Given and

a + b = 16 and ab = 25

S = sum of roots = a + b = 16.

and P = Product of roots = ab = 25

∴ Required quadratic equation is or

Write first five terms of the following sequence and obtain the corresponding series.

for all n>1

Write first five terms of the following sequence and obtain the corresponding series.

, n>2

Show that the sequence defined by (where A and B are constant) is an A.P. with common difference A.

Show that the sequence defined by is not an A.P.

Which term of an A.P. 5, 2, -1, ......... is -22?

Which term of the sequence 12 + 8i, 11 + 6i, 10+41i, ....... is

(i) purely real (ii) purely imaginary?

Which term of the sequence is the first negative term?

Determine the number of terms in an A.P. 3, 8, 13, .......253. Also, find 12th term from the end.

Find the 2nd term and the rth term of an A.P. whose 6th term is 12 and 8th term is 22.

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.