SEQUENCES AND SERIES — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES2 Marks
Question
Insert five numbers between 8 and 26 so that the resulting sequence is an A.P.
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Answer
Let $A_1, A_2, A_3, A_4$ and $A_5$ be five numbers between 8 and 26 such that $8, A_1, A_2, A_3, A_4, A_5, 26$ are in $A_1 P$ Here, $\mathrm{a}=8$ and $\mathrm{a}_7=26$ and let d be the common difference.
$\therefore a_7=a+(7-1) d=26$
$\Rightarrow 8+6 d=26$
$\Rightarrow 6 d=18$
$\Rightarrow d=3$
Now, $A_1=a+d=8+3=11$
$A_2=a+2 d=8+2 \times 3=8+6=14$
$A_3=a+3 d=8+3 \times 3=8+9=17$
$A_4=a+4 d=8+4 \times 3=8+12=20$
$A_5=a+5 d=8+5 \times 3=8+15=23$
Hence the five numbers are $11,14,17,20$ and 23
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