The sum of all integers between $1$ and $100$ (both inclusive) which are divisible by $5$ or $13$ is

Find the mean of the first $n$ terms of the $A$.$P$. $a, (a + d), (a + 2d), \dots$

Let $S = \{(a, b, c) \in \mathbb{N} \times \mathbb{N} \times \mathbb{N} : a+b+c=21, a \leq b \leq c\}$ and $T = \{(a, b, c) \in \mathbb{N} \times \mathbb{N} \times \mathbb{N} : a, b, c \text{ are in } AP\}$, where $\mathbb{N}$ is the set of all natural numbers. Then, the number of elements in the set $S \cap T$ is:

The first term of an $A.P.$ is $2$ and the common difference is $4$. The sum of its $40$ terms will be:

If $a_1, a_2, a_3, \dots, a_n$ are in $A.P.$ and $a_1 + a_4 + a_7 + \dots + a_{16} = 114$,then $a_1 + a_6 + a_{11} + a_{16}$ is equal to

If the sum of three numbers in an $A.P.$ is $24$ and their product is $440,$ find the numbers.