Find the sum of the following $APs$: $0.6, 1.7, 2.8, \ldots,$ to $100$ terms.

  • A
    $5505$
  • B
    $5402$
  • C
    $5621$
  • D
    $5586$

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For the $AP: \frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots,$ write the first term $a$ and the common difference $d$.

Find the sum of the following $APs$: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \ldots,$ to $11$ terms.

$A$ spiral is made up of successive semicircles,with centres alternately at $A$ and $B$,starting with centre at $A$,of radii $0.5 \, cm, 1.0 \, cm, 1.5 \, cm, 2.0 \, cm, \ldots$ as shown in the figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take $\pi = \frac{22}{7}$)

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Fill in the blanks in the following table,given that $a$ is the first term,$d$ is the common difference,and $a_{n}$ is the $n^{th}$ term of the $AP$:
$S.No.$$a$$d$$n$$a_{n}$
$(i)$$7$$3$$8$$...$
$(ii)$$-18$$...$$10$$0$
$(iii)$$...$$-3$$18$$-5$
$(iv)$$-18.9$$2.5$$...$$3.6$
$(v)$$3.5$$0$$105$$...$

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$A$ small terrace at a football ground comprises of $15$ steps each of which is $50 \, m$ long and built of solid concrete. Each step has a rise of $\frac{1}{4} \, m$ and a tread of $\frac{1}{2} \, m$. Calculate the total volume of concrete required to build the terrace (in $m^3$).

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