Question

find number of terms in the AP
a.25 , 30 , 35 , 40 , .......... 120​

Answer 1

To Find :

• we need to find number of terms.

Given :

• AP = 25 , 30 ,35 ,40 ......120

First term (a) = 25

common difference (d) = a2 - a1

• a2 = 30
• a1 = 25

= 30 - 25

= 5

• a3 - a2
• a3 = 35
• a2 = 30

= 35 - 30

= 5

• So, common difference (d) = 5

Last term = 120

we know that,

• 《 an = a + (n - 1)d 》
• an = 120
• a = 25
• d = 5
• n = ?

⇛120 = 25 + (n - 1)5

⇛ 120 - 25 = 5n - 5

⇛ 95 = 5n - 5

⇛ 95 + 5 = 5n

⇛ 100 = 5n

⇛ n = 100/5

⇛ n = 20

Hence,

• Number of term in given AP = 20

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Answer 2

$\huge\sf\pink{Answer}$

☞ There are 20 terms innthe AP

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$\huge\sf\blue{Given}$

✭ AP - 25,30,35,40..... 120

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

◈ Number of terms in the AP?

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$\huge\sf\purple{Steps}$

So here we shall use the formula,

$\underline{\boxed{\red{\sf a_n = a+(n-1)d}}}$

Here,

➝ $\sf a_n = 120$

➝ $\sf a = 25$

➝ $\sf d = a_2 - a_1$

➝ $\sf d = 30-25 = 5$

Substituting the given values,

➳ $\sf a_n = a+(n-1)d$

➳ $\sf 120 = 25+(n-1)(5)$

➳ $\sf 120-25 = (n-1)(5)$

➳ $\sf 95 = (n-1)(5)$

➳ $\sf \dfrac{95}{5} = n-1$

➳ $\sf 19 = n-1$

➳ $\sf 19+1 = n$

➳ $\sf\orange{n = 20}$

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