8. If $10$ times the ${{10}^{th}}$ term of an A.P. is equal to $15$ times the ${{15}^{th}}$ term, show that ${{25}^{th}}$ term of the A.P. is zero. - Noon Academy

8. If $10$ times the ${{10}^{th}}$ term of an A.P. is equal to $15$ times the ${{15}^{th}}$ term, show that ${{25}^{th}}$ term of the A.P. is zero.

Arithmetic Progression | Class 10 | ICSE | Maths | RD Sharma

8. If $10$ times the ${{10}^{th}}$ term of an A.P. is equal to $15$ times the ${{15}^{th}}$ term, show that ${{25}^{th}}$ term of the A.P. is zero.

An arithmetic progression or arithmetic sequence is a number’s sequence such that the difference between the consecutive terms is constant.

Solutions:

Given,

times the ${{10}^{th}}$ term of an A.P. is equal to $15$ times the ${{15}^{th}}$ term.

We know that, ${{n}^{th}}$ term ${{a}_{n}}=a+\left( n-1 \right)d$

⇒ $10\left( {{a}_{10}} \right)=15\left( {{a}_{15}} \right)$

$10\left( a+\left( 10-1 \right)d \right)=15\left( a+\left( 15-1 \right)d \right)$

$10\left( a+9d \right)=15\left( a+14d \right)$

$10a+90d=15a+210d$

$5a+120d=0$

$5\left( a+24d \right)=0$

$a+24d=0$

$a+\left( 25-1 \right)d=0$

⇒ ${{a}_{25}}=0$

Therefore, the ${{25}^{th}}$ term of the A.P. is zero.

i

More Material

Write chromyl chloride test with equation

What do you understand by lanthanide contraction

What are lanthanide elements?

Explain oxidization properties of potassium permanganate in acidic medium.

A …… lens is used to correct myopia and a ….. lens is used to correct hypermetropia.
A Concave, concave
B Convex, convex
C Convex, concave
D Concave, convex

Rate of reaction of any substance depends on
(A) active mass
(B) molecular weight
(C) atomic weight
(D) equivalent weight

Formula of oleum is
(A) $\mathrm{H}_{2} \mathrm{~S}_{2} \mathrm{O}_{7}$
(B) $\mathrm{H}_{2} \mathrm{SO}_{4}$
(C) $\mathrm{H}_{2} \mathrm{SO}_{3}$
(D) $\mathrm{H}_{2} \mathrm{SO}_{5}$

Give two differences between double salt and complex salt.

Give two differences between DNA and RNA.

Find the shortest distance between the given lines.
$\begin{array}{l} \square \vec{r}=(\hat{i}+\hat{j})+\lambda(2 \hat{i}-\hat{j}+\hat{k}) \\ \vec{r}=(2 \hat{i}+\hat{j}-\hat{k})+\mu(3 \hat{i}-5 \hat{j}+2 \hat{k}) \end{array}$

Which of the following compounds has tetrahedral geometry? (a) $\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{-2}$ (b) $\left[\mathrm{Pd}(\mathrm{CN})_{4}\right]^{2-}$ (c) $\left[\mathrm{PdCl}_{4}\right]^{2-}$ (d) $\left[\mathrm{NiCl}_{4}\right]^{2}$

Oxidation number of gold metal is (a)+1 (b) 0 (c) $-1$ (d) all of these

← Previous Next →