Question

No spam


Chapter Name = Arithmetic Progression​

Answer 1

Step-by-step explanation:

I hope this will helps you.

Answer 2

Answer:

Given :

The nᵗʰ term of ap is 3, 8, 14, 18 is 73.

To Find :

The value of n.

Using Formula :

$\star \:\underline{\boxed{\sf{\pink{d = a_2 - a_1}}}}$

• $\rm{d}$ = common difference
• $\rm{a_1}$ = first term
• $\rm{a_2}$ = second term

$\star \:\underline{\boxed{\sf{\pink{a_n =a_1 + \bigg(n - 1 \bigg)d}}}}$

• $\rm{a_n}$ = the nᵗʰ term 
• $\rm{a}$ = first term
• $\rm{n}$ = number of terms
• $\rm{d}$ = common difference

Solution :

Firstly, finding the common difference between the consecutive terms.

${\implies{\sf{d = a_2 - a_1}}}$

${\implies{\sf{d = 8 - 5}}}$

${\implies{\sf{\underline{\underline{\red{d = 3}}}}}}$

Hence, the common difference between the terms is 3.

$\rule{300}{1.5}$

Now, finding the value of n by substituting the values in the formula :

${\implies{\sf{a_n =a_1 + \bigg(n - 1 \bigg)d}}}$

${\implies{\sf{73=3 + \bigg(n - 1 \bigg)5}}}$

${\implies{\sf{73 - 3=\bigg(n - 1 \bigg)5}}}$

${\implies{\sf{70=\bigg(n - 1 \bigg)5}}}$

${\implies{\sf{70=5n - 5}}}$

${\implies{\sf{5n = 70 + 5}}}$

${\implies{\sf{5n = 75}}}$

${\implies{\sf{n = \dfrac{75}{5}}}}$

${\implies{\sf{n = \cancel{\dfrac{75}{5}}}}}$

${\implies{\sf{\underline{\underline{\red{n = 15}}}}}}$

Hence, the value of n is 5.

$\rule{220pt}{2.5pt}$

Learn More :

★ Formula to find the numbers of term of an AP:

$\longrightarrow{\small{\underline{\boxed{\sf{\purple{n= \bigg[ \dfrac{(l - a)}{d} \bigg]}}}}}}$

★ Formula to find the tsum of first n terms of an AP:

$\longrightarrow{\small{\underline{\boxed{\sf{\purple{S_n= \dfrac{n}{2} \big(a + l \big)}}}}}}$

★ Formula to find the sum of squares of first n natural numbers of an AP:

$\longrightarrow{\small{\underline{\boxed{\sf{\purple{S = \dfrac{n(n + 1)(2n + 1)}{6} }}}}}}$

★ Formula to find the nth term of an AP is the square of the number of terms:

$\longrightarrow{\small{\underline{\boxed{\sf{\purple{S = {(n)}^{2} }}}}}}$

★ Formula to find the sum of of an AP:

$\longrightarrow{\small{\underline{\boxed{\sf{\purple{S = n(n+1)}}}}}}$

${\rule{220pt}{3pt}}$