Question
How many terms are there in the $A.P.?$
$7, 13, 19, ....., 205.$
$7, 13, 19, ....., 205.$
✓
Answer
Given,$A.P. 7, 13, 19, ....., 205$
Here,
First term, $a = 7,$
Difference $d = 13 - 7 = 6$
Last $n^{th}$ term $a_n = 205$
We know, $n^{th}$ term of $A.P.$
$a_n = a + (n - 1)d$
$\Rightarrow 205 = 7 + (n - 1)6$
$\Rightarrow 205 = 7 + 6n - 6$
$\Rightarrow 205 = 1 + 6n$
$\Rightarrow 6n = 204$
$\Rightarrow\ \text{n}=\frac{204}{6}$
$\Rightarrow n = 34$
Hence, Total $34$ terms in given $A.P.$
Here,
First term, $a = 7,$
Difference $d = 13 - 7 = 6$
Last $n^{th}$ term $a_n = 205$
We know, $n^{th}$ term of $A.P.$
$a_n = a + (n - 1)d$
$\Rightarrow 205 = 7 + (n - 1)6$
$\Rightarrow 205 = 7 + 6n - 6$
$\Rightarrow 205 = 1 + 6n$
$\Rightarrow 6n = 204$
$\Rightarrow\ \text{n}=\frac{204}{6}$
$\Rightarrow n = 34$
Hence, Total $34$ terms in given $A.P.$
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
If n is an odd integer, then show that $n^2 - 1$ is divisible by 8.
→A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are respectively 30° and 60°. Find the height of the tower.
In the following figure find the area of the shaded region. $\big(\text{Use }\pi=3.14\big)$
→If the points $A(1,2), O(0,0)$ and $C(a, b)$ are collinear, then find $a: b$.
→Find the area of the circle in which a square of area $64 cm^2$ is inscribed. [Use $\pi=3.14$ ]
→Very-Short and Short-Answer Questions:
Solve $\frac{3}{\text{x}+\text{y}}+\frac{2}{\text{x}-\text{y}}=2$ and $\frac{9}{\text{x}+\text{y}}-\frac{4}{\text{x}-\text{y}}=1$
→Solve $\frac{3}{\text{x}+\text{y}}+\frac{2}{\text{x}-\text{y}}=2$ and $\frac{9}{\text{x}+\text{y}}-\frac{4}{\text{x}-\text{y}}=1$
If the sum of first p term of an A.P. is $ap^2 + bp$, find its common difference.
→Half the perimeter of a garden, whose length is 4 more than its width is 36m. Find the dimension of the garden.
An oil funnel of tin sheet consists of a cylindrical portion $10\ cm$ long attached to a frustum of a cone. If the total height be $22\ cm$, the diameter of the cylindrical portion 8cm and the diameter of the top of the funnel $18\ cm$, find the area of the tin required.
→In fig, $\triangle \text{PQR}$ is, right angled at $\text{Q , QR }=6 \ cm$, $\angle \text{QPR}=60^{\circ}$. Find the length of $PQ$ and $PR .$
→