Question

Solution

Let a - d, a, a + d be three numbers in A.P. Since their sum is 21

∴ a - d + a + a + d = 21

3a = 21 a = 7

∴ Numbers are 7 - d, 7, 7 + d

It is given that if the second number is reduced by 1 and third is increased by 1 then resulting three numbers form G.P.

∴ 7 - d, 7 - 1, 7 + d + 1 are in G.P. or 7 - d, 6, 8 + d are in G.P.

(8 + d) (7 - d) = 36

56 - 8d + 7d - d^{2} = 36

d =

When a = 7 and d = 4, numbers are 7 - 4, 7 + 4 or 3, 7, 11

when a = 7 and d = -5, numbers are 7 - (-5), 7, 7 - 5 or 12, 7, 2

Consider the sequence defined by t_{n} = an^{2} + bn + c. If t_{2} = 3, t_{4} = 13 and t_{7} = 113, show that 3t_{n} = 17n^{2} – 87n + 115

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.