Maharashtra BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
Question
Find the common difference of the A.P. and write the next two terms:
$51, 59, 67, 75, .....$
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Answer
$51,59,67,75, \ldots .$.
Here,
$a_1=51$
$a_2=59$
So, common difference of the A.P. (d) $=a_2-a_1$
$=59-51$
$=8$
Also, we need to find the next two terms of A.P., which means we have to find the $5^{\text {th }}$ and $6^{\text {th }}$ term. So, for fifth term,
$a_5=a_1+4 d$
$=51+4(8)$
$=51+32$
$=83$
Similarly, we find the sixth term,
$a_6=a_1+5 d$
$=51+5(8)$
$=51+40$
$=91$
Therefore, the common difference is $d=8$ and the next two terms of the A.P. are $a_5=83, a_6=91$.
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