Find the sum:7+101 2 +14+ ..... + 84 - Vidyadip

Question

Find the sum:$\text{7}+10\frac{1}{2}+14+\ .....\ + 84$

✓

Answer

Given,
$\text{A.P., }7+10\frac{1}{2}+14+\ .....\ + 84$
Here,
First term, a = 7
Difference, $\text{d}=\frac{21}{2}-7=\frac{7}{2}$
and Last term, $a_n = 84$
We know, $a_n = a + (n - 1)d$
$\Rightarrow\ 84= 7 + (\text{n}-1)\frac{7}{2}$
$\Rightarrow\ 84=7+\frac{7\text{n}}{2}-\frac{7}{2}$
$\Rightarrow\ 84=\frac{14+7\text{n}-7}{2}$
$\Rightarrow\ 84\times2=7+7\text{n}$
$\Rightarrow\ 168=7+7\text{n}$
$\Rightarrow\ 7\text{n}=168-7$
$\Rightarrow\ \text{n}=\frac{161}{7}=23$
We know, Sum of n terms,
$\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]$
$\Rightarrow\ \text{S}_{23}=\frac{23}{2}\Big[2(7)+(23-1)\frac{7}{2}\Big]$
$\Rightarrow\ \text{S}_{23}=\frac{23}{2}\Big[14+22\times\frac{7}{2}\Big]$
$\Rightarrow\ \text{S}_{23}=\frac{23}{2}[14+77]$
$\Rightarrow\ \text{S}_{23}=\frac{23}{2}\times91=\frac{2093}{2}$
Hecne, Sum of given A.P. is $\frac{2093}{2}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Arithmetic Progressions→Arithmetic Progressions — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Two different dice are rolled simultanceously. Find the probability that the sum of the numbers on the two dice is 10.

Evaluate the following:
If $\tan(\text{A}-\text{B})=\frac{1}{\sqrt{3}}$ and $\tan(\text{A}+\text{B})=\sqrt{3},0^\circ<(\text{A}+\text{B})\leq90^\circ$ and $\text{A}>\text{B}$ then find A and B.

Find the common difference and write the next four terms of the following arithmetic progressions:
$-1,\frac{5}{6},\frac{2}{3},\ .....$

Solve the following pairs of equations:
$\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=\text{a}+\text{b},\frac{\text{x}}{\text{a}^2}+\frac{\text{y}}{\text{b}^2}=2\text{ a},\text{ b}\neq0$

On selling a tea at 5% loss and a lemon set at 15% gain, a crockery seller gains ₹7. If he sells the tea set at 5% gain and the lemon set at 10% gain, he gains ₹13. Find the actual price of each of the tea set and the lemon set.

The centre of a circle is (2a, a - 7). Find the values of a if the circle passes through the point (11, -9) and has diameter $10\sqrt{2}$ units.

Calculate the median from the following frequency distribution:

Class	5-10	10-15	15-20	20-25	20-30	30-35	35-40	40-45
Frequency	5	6	15	10	5	4	2	2

Draw a ΔABC in which BC = 6cm, AB = 4cm and AC = 5cm. Draw a triangle similar to $\triangle\text{ABC}.$ with its sides equal to $\Big(\frac{3}{4}\Big)^\text{th}$ of the corresponding sides of $\triangle\text{ABC}.$

Find mode of the following data:

Classes	0-20	20-40	40-60	60-80	80-100	100-120	120-140
Frequency	6	8	10	12	6	5	3

In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by $100 km / h$ and time increased by 30 minutes. Find the original duration of the flight.