CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions2 Marks
Question
Find $a _{30}- a _{20}$ for the A.P.
$a, a+d, a+2 d, a+3 d, \ldots . .$
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Answer
Given,
$a_{30}-a_{20}=a+(30-1) d-(a+(20-1) d)\left(\therefore a_n=a+(n-1) d\right)$
$=a+29 d-a-19 d$
$=10 d$
In $A.P. a, a + d, a + 2d, a + 3d, .....$
$a$ is the first term and $d$ is the common difference
$\therefore$ $a_n = a + (n - 1)d$
$\therefore$ $a_{20} = a + (20 - 1)d = a + 19d$
and $a_{30} = a + (30 - 1)d = a + 29d$
$\therefore$ $a_{30} - a_{20} =a + 29d - a - 19d = 10d.$
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