Question
How many term are there in the $AP 6, 10, 14, 18,....174?$
✓
Answer
In the given $AP,$ we have $a = 6$ and $d = (10 - 6) = 4$
Suppose there are n term in the given $AP,$ then
$T_n= 174 ⇒ a + (n - 1)d = 174$
$⇒ 6 + (n - 1)4 = 174$
$⇒ 6 + 4n - 4 = 174$
$⇒ 2 + 4n = 174 ⇒ \text{n}=\frac{172}{4}=43$
Hence there are $43$ terms in the given $AP$
Suppose there are n term in the given $AP,$ then
$T_n= 174 ⇒ a + (n - 1)d = 174$
$⇒ 6 + (n - 1)4 = 174$
$⇒ 6 + 4n - 4 = 174$
$⇒ 2 + 4n = 174 ⇒ \text{n}=\frac{172}{4}=43$
Hence there are $43$ terms in the given $AP$
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 in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar:
The volume of a sphere is $4851\ cm^3$. Find its curved surface area.
→If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = x^2- x - 4,$ find the value of $\frac{1}{\alpha}+\frac{1}{\beta}-\alpha\beta$
→Find the zeroes of quadratic polynomial $6x^2 - 3 - 7x$ and verify the relationship between the zeroes and their coefficients.
→In the given figure, $PQ$ is tangent at a point $R$ of the circle with centre $O.$ If $\angle\text{TRQ}=30^{\circ},$ find $m$ $\angle\text{PRS}$.
→Very-Short and Short-Answer Questions:
Write the number of solutions of the following pair of linear equations:
$x + 2y - 8 = 0,$
$2x + 4y = 16$
→Write the number of solutions of the following pair of linear equations:
$x + 2y - 8 = 0,$
$2x + 4y = 16$
Apply division algorithm to find the quotient $q(x)$ and remainder $r(x)$ in dividing $f(x)$ by $g(x)$ in the following:
$ f(x)=4 x^3+8 x+8 x^2+7, g(x)=2 x^2-x+1 $
→$ f(x)=4 x^3+8 x+8 x^2+7, g(x)=2 x^2-x+1 $
All integers between $1$ and $500$ which are multiplies of $2$ as well as of $5.$
→The angle of elevation of the top of a building from the foot of the tower is $30^\circ $ and the angle of elevation of the top of the tower from the foot of the building is $60^\circ $. If the tower is $50\ m$ high, find the height of the building.
→IfA and B are (-2,-2) and (2,-4) respectively, find the coordinates of P such that $AP =\frac{3}{7}$ and P lies on the line segment AB.
→