In an $AP$ given $a=7$ and $a_{13}=35$,find $d$ and $S_{13}$.

In the following $APs,$ find the missing term in the box: $2, \square, 26$

Ramkali saved ₹ $5$ in the first week of a year and then increased her weekly savings by ₹ $1.75$. If in the $n$-th week,her weekly savings become ₹ $20.75$,find $n$.

Find the sum given below: $34 + 32 + 30 + \ldots + 10$

In which of the following situations,does the list of numbers involved make an arithmetic progression,and why? The amount of money in the account every year,when ₹ $10000$ is deposited at compound interest at $8 \%$ per annum.

$A$ 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 $\pi = \frac{22}{7}$)