# CLASS-10GEOMETRIC PROGRESSION - FINDING e-TERM FROM END OF G.P.

e-th Term From The End of G.P.

Theorem.2) In a given G.P. let the first term be ‘a’, common ratio be ‘r’, and the last term be ‘l’.

l

Then its e-th term from the end is given by -------

r⁽ᵉˉ¹⁾

Proof.- In a given G.P. let the first term be ‘a’, common ratio be ‘r’, and the last term be ‘l

Then,

l           l

2nd term from the end = ------ = -------

r          r⁽²ˉ¹⁾

l            l

3rd term from the end = ------- = -------

r²          r⁽³ˉ¹⁾

l            l

4th term from the end = ------- = -------

r³          r⁽⁴ˉ¹⁾

l            l

5th term from the end = ------- = -------

r⁴           r⁽⁵ˉ¹⁾

………….…   …..…………    ……………….

…………….   ……………...   ……………….

l

e-th term from the end = ------

r⁽ᵉˉ¹⁾

l

Hence the e-th term from the end is ------

r⁽ᵉˉ¹⁾

Example.1) Find the 10th term from the end of the G.P. 3, 6, 12, 24,……….,6144

Ans.) Given G.P. is 3, 6, 12, 24,…………………., 6144

6

Here, a = 3, r = ----- = 2, l = 6144

3

l          6144

10th term from the end = ------ = ---------

r⁽ᵉˉ¹⁾       2⁽¹⁰ˉ¹⁾

6144

= ----------

2⁹

6144

= ---------

512

=    12

Hence the 10th term from the end is 12    (Ans.)