SEQUENCES AND SERIES — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES1 Mark
Question
Insert 6 numbers between 3 and 24 such that the resulting sequence is an A.P.
✓
Answer
Let $A_1, A_2, A_3, A_4, A_5$ and $A_6$ be six numbers between 3 and 24 such that $3, A_1, A_2, A_3, A_4, A_5, A_6, 24$ are in $A . P$. Here, a $=3, b=24, n=8$.
Thus, $24=3+(8-1) d$, so that $d=3$.
Therefore, A1 = $a+d=3+3=6$;
$A_2=a+2 d=3+2 \times 3=9$
$A_3=a+3 d=3+3 \times 3=12$
$A_4=a+4 d=3+4 \times 3=15$
$A_5=a+5 d=3+5 \times 3=18$
$A_6=a+6 d=3+6 \times 3=21$
Therefore,six numbers between 3 and 24 are 6, 9, 12, 15, 18 and 21.
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