CBSEi Class 10 Sequences (AP and GP) CORE
CBSEi Class 10 Sequences (AP and GP) CORE
CBSEi Class 10 Sequences (AP and GP) CORE
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The fixed number is called the common ratio of the progression <strong>and</strong> is usually denoted<br />
by r. Thus in (i), common ratio (r) is 2 <strong>and</strong> in (ii) common ratio (r) is .<br />
The first term of a geometric progression (<strong>GP</strong>) is usually written as a (as in case of <strong>AP</strong>).<br />
Thus, in general.<br />
If a is the first term <strong>and</strong> r, the common ratio of a <strong>GP</strong>, then <strong>GP</strong> can be written as<br />
a, ar, ar 2 , ar 3 , ….<br />
Note that in case of a <strong>GP</strong>,<br />
Common ratio<br />
=<br />
=<br />
=<br />
<strong>and</strong> so on.<br />
Example 15: Identify which of the following are geometric progressions. For those<br />
Solution:<br />
which are geometric progressions, find the common ratios:<br />
(i) 3, 6, 12, 24, ……<br />
(ii)<br />
1 1 1 1<br />
, , , ,............<br />
3 9 27 81<br />
(iii) 2, 6, 18, 54<br />
(iv)<br />
4 8 16 32<br />
, , , ,............<br />
3 5 7 9<br />
(i) 3, 6, 12, 24, …..<br />
Here a = 3. We have<br />
53
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