Short Answer TypeWhich term of the sequence 12 + 8i, 11 + 6i, 10+41i, ....... is
(i) purely real (ii) purely imaginary?
The given sequence is :
12 + 8i, 11 + 6i, 10+4i, .......
Here, a = 12 + 8i
d = (11 + 6i) - (12 + 8i) = -1 - 2i
(i) Let nth term be purely real
∴ 
is purely real
or 12 + 8i + (n - 1) (-1 - 2i) is purely real
or 12 + 8i - (n - 1) - 2 (n - 1) is purely real
or (13 - n) + (10 - 2n) i is purely real
∴ 10 - 2n = 0 or n = 5
∴ 5th term is purely real.
(ii) Let nth term be purely imaginary
∴ 
is purely imaginary
or (13 - n) + (10 - 2n) is purely imaginary
or 13 - n = 0
or n = 13
∴ 13th term is purely imaginary.
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.
Long Answer TypeShort Answer TypeIf m times the mth term is equal to n times the nth term of an A.P. Prove that (m + w)th term of an A.P. is zero.
If (m + l)th term of an A.P. is twice the (n + l)th term. Prove that (3m + l)th term is twice the (m + n + l)th term.
defined by 
is not an A.P.
Switch
is the first negative term?
and the nth term is 
find the (mn)th term.
