CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
Question
Determine the $AP$ whose fifth term is $19 $and the difference of the eighth term from the thirteenth term is $20.$
✓
Answer
Let the first term of an AP be a and common difference d.
Given, $a_5 = 19$ and $a_{13} - a_8= 20$ [given]
[$\because$ $a_n = a + (n - 1)d]$
$\Rightarrow a_5 = a + (5 - 1)d = 19 .......(i)$
and $[a + (13 - 1)d] - [a + (8 - 1)d] = 20$
and $a + 12d - a - 7d = 20$
$\Rightarrow 5d = 20$
$\therefore$ $d = 4$
On putting $d = 4$ in Eq. (i), we get
$a + 4(4) = 19$
$\Rightarrow a + 16 = 19$
$\Rightarrow a = 19 - 16$
$\Rightarrow a = 3$
so, required AP is a, $a + d, a + 2d, a + 3d, .....$
$i.e., 3, 3 + 4, 3 + 2(4), 3 + 3(4), ......$
$i.e., 3, 7, 11, 15, ......$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.