Question
Write the value of $a_{30} - a_{10}$_ for the A.P. $4, 9, 14, 19, .....$
✓
Answer
Given,
A.P. $4, 9, 14, 19, .....$
Here, First term $a = 4$
and Difference $d = 9 - 4 = 5$
We know,
$a_n = a + (n - 1)d$
$30^{th}$ term
$a_{30} = 4 + (30 - 1)5$
$\Rightarrow a_{30} = 4 + 29 \times 5$
$\Rightarrow a_{30} = 4 + 145$
$\Rightarrow a_{30} = 149$
$10^{th}$^ term,
$a_{10} = 4 + (10 - 1)5$
$\Rightarrow a_{10} = 4 + 9 \times 5$
$\Rightarrow a_{10} = 4 + 45$
$\Rightarrow a_{10} = 49$
Now, we have to find $a_{30} - a_{10}$_
Now, we have to find $a_{30} - a_{10}$_
$\Rightarrow a_{30} - a_{10} = 149 - 49$
$\Rightarrow a_{30} - a_{10} = 100$
Hence, value of $a_{30} - a_{10}$_ is $100.$
A.P. $4, 9, 14, 19, .....$
Here, First term $a = 4$
and Difference $d = 9 - 4 = 5$
We know,
$a_n = a + (n - 1)d$
$30^{th}$ term
$a_{30} = 4 + (30 - 1)5$
$\Rightarrow a_{30} = 4 + 29 \times 5$
$\Rightarrow a_{30} = 4 + 145$
$\Rightarrow a_{30} = 149$
$10^{th}$^ term,
$a_{10} = 4 + (10 - 1)5$
$\Rightarrow a_{10} = 4 + 9 \times 5$
$\Rightarrow a_{10} = 4 + 45$
$\Rightarrow a_{10} = 49$
Now, we have to find $a_{30} - a_{10}$_
Now, we have to find $a_{30} - a_{10}$_
$\Rightarrow a_{30} - a_{10} = 149 - 49$
$\Rightarrow a_{30} - a_{10} = 100$
Hence, value of $a_{30} - a_{10}$_ is $100.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Prove the following.
$\frac{\sin \theta-\cos \theta+1}{\sin \theta+\cos \theta-1}=\frac{1}{\sec \theta-\tan \theta}$
→$\frac{\sin \theta-\cos \theta+1}{\sin \theta+\cos \theta-1}=\frac{1}{\sec \theta-\tan \theta}$
The marks scored by 750 students in an examination are given in the form of a frequency distribution table:
Prepare a cumulative frequency table by less than method and
draw on ogive.
|
Marks
|
No. of students
|
|
600-640
|
16
|
|
640-680
|
45
|
|
680-720
|
156
|
|
720-760
|
284
|
|
760-800
|
172
|
|
800-840
|
59
|
|
840-880
|
18
|
draw on ogive.
12,16,20,24………Find 25th term of this A.P.
The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its
i) Curved surface area
ii) Total surface area
iii) Volume
i) Curved surface area
ii) Total surface area
iii) Volume
Prove the following trigonometric identities.
$(1+\cot\text{A}-\text{cosec A})(1+\tan\text{A}+\sec\text{A})=2$
→→$(1+\cot\text{A}-\text{cosec A})(1+\tan\text{A}+\sec\text{A})=2$
The angle of depression from the top of a tower of a point A on the ground is 30°. On moving a distance of 20 metres from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower from the point B is 60°. Find the height of the tower and its distance from the point A.
In $\triangle\text{ABC}$ (Fig.), if $\angle1=\angle2,$ prove that $\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}}.$
→From a rectangular sheet of paper ABCD with $AB = 40\ cm$ and $AD = 28\ cm$, a semicircular portion with BC as diameter is cut off. Find the area of the remaining paper.
→In the adjoining figure, point O is the centre of the circle. Line PB is a tangent and line PAC is a secant. Find PA × PC if OP = 25 and radius is 7.
