Question

The 5th team of an arithmetic sequence is 38 and 9th team is 66 what is 25th team by using equation xn

Answer 1

$\huge\sf\pink{Answer}$

☞ 25th term is 178

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$\huge\sf\blue{Given}$

✭ The 5th term of an AP - 38

✭ The 9th term of an AP - 66

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$\huge\sf\gray{To \:Find}$

◈ The 25 th term?

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$\huge\sf\purple{Steps}$

$\bullet\:\underline{\textsf{ As Per the Question}}$

◕ $\sf a_5 = 38$

◕ $\sf a_9 = 66$

We know that,

➝ $\sf a_5 = a+4d=38\quad -eq(1)$

➝ $\sf a_9 = a+8d=66\quad -eq(2)$

Subtracting eq (1) from eq(2)

$\sf a + 8d = 66 \\ \sf a + 4d = 38 \\ \underline{ \qquad \qquad \qquad} \\ \sf \qquad 4d = 28$

➢ $\sf d = \dfrac{28}{4}$

➢ $\sf\red{d = 7}$

Substituting value of a in eq(1)

»» $\sf a+4(7)=38$

»» $\sf a+28 =38$

»» $\sf a =38-28$

»» $\sf\green{a =10}$

Now,the 25th term will be,

➳ $\sf a_{25} = a+24d$

➳ $\sf a_{25} = 10+24(7)$

➳ $\sf\orange{a_{25} = 178}$

$\rule{170}3$

Answer 2

Answer:

a25=178

Step-by-step explanation:

a+(n-1)d=an

a+(5-1)d=a5

a+(5-1)d=38

a+4d=38(1)

similarly

a+8d=66(2)

(1)-(2)

d=7

a+4d=28

a+28=38

a=10

a25=10+(25-1)7

a25=10+(24×7)

a25=168+10

a25=178