Sum of First n Terms of an AP

The sum of $n$ terms of an A.P. is $3n^2+5n$, then its first term is

The sum of the first $100$ natural numbers is

Sachin invested some amounts in National Saving Certificates in a specific way. In the first year he invested $₹4,000$, in the second year $₹6,000$, in the third year $₹8,000$ and so on for $12$ years. Find the total amount (in $₹$) he invested in $12$ years.

Find the sum of the series $3+7+11+ .......$ to $10$ terms.

Find the sum of all two digit positive integers which are divisible by $3$ but not by $2$.

Find the sum of the first twenty terms of Arithmetic series $2+7+12+...$ 

Sum of all the first $\text{'}n\text{'}$ terms of even natural number is

If second and third terms of an Arithmetic Progression are $3$ and $5$ respectively, then find the sum of first $20$ terms of it.

For an A.P., find $S_{10}$ if $a=6$ and $d=3$.

If $S_5=15$ and $S_6=21$, find $t_6$.

Find the sum of all two-digit odd multiples of $3$. 

Sachin invested some amounts in National Saving Certificates in a specific way. In the first year he invested $₹4,000$ in the second year $₹6,000$ in the third year $₹8,000$ and so on for $12$ years. Find the total amount (in $₹$) he invested in $12$ years.

Find the sum of $5+8+11+...$ upto $10$ terms.

Find the sum of all the natural numbers divisible by $5$ between $2$ and $101$

The distance between $A$ and $B$ is $125 \mathrm{km}$ and there are eight($8$) traffic signals in between $A$ and $B$. If a car by $50 \mathrm{km}/\mathrm{h}$ speed reaches point $B$ crossing all green signals in $2$ hours and $30$ minutes but on other days due to heavy traffic it happens to stop as follows.

First Traffic Signal $- 1$ minute, Second Traffic Signal $- 2$ minutes and upto Eighth  signal $- 8$ minutes. Calculate the total time taken (in minutes) by that car if it follows the total traffic signals.

If second and third terms of an A.P. are $24$ and $28$ respectively, then find the sum of first $61$ terms.

Houses in a row are numbered serially from $1$ to $49$. Show that one value of $x$ in such that the sum of numbers of houses preceding the marked house is equal to the sum of numbers of houses succeeding the marked house. Find the value of $x$.

A sum of $₹280$ is to be used to give four prizes. If each prize is $₹20$ less than its preceding prize. Find the value of each of the prizes.

First term of an arithmetic progression is $8$, $n^{th}$ term is $33$ and sum of first $n$ terms is $123$, then find $n$ and common difference $d$

First and last term of A.P are $17$ and $350$ respectively. If common difference is $9$ then how many terms are there in A.P. Find their sum?