Question

Find the number of terms in A.P 4, 7, 10, 13 .............148 ?​

Answer 1

Answer:

→49.

Step-by-step explanation:

Given AP is 4,7,10,13,...148

First term = 4

Common difference =7-4 = 3

Let nth term = 148

We know that

nth term of an AP = an = a+(n-1)d

Now,

an = 148

⇛4+(n-1)(3) = 148

⇛4+3n-3 = 148

⇛3n+1 = 148

⇛3n = 148-1

⇛3n = 147

⇛n = 147/3

⇛n = 49

Number of terms in the AP = 49

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Answer 2

Answer:

The number of terms is 49.

Step-by-step explanation:

Solution :

Here we have provided that :

• $\small\purple{\bull}$ First term (a) = 4
• $\small\purple{\bull}$ nth term of ap (aₙ) = 148
• $\small\purple{\bull}$ Common difference (d) = 7 - 4 = 3

We need to find :

• $\small\purple{\bull}$ Number of terms

Here's the required formula to find the number of terms :

$\longrightarrow{\pmb{\sf{a_{n} = a + \big(n - 1\big)d}}}$

• $\pink \star$ aₙ = nth term of ap
• $\pink\star$ a = first term
• $\pink\star$ n = number of term
• $\pink\star$ d = common difference

Substituting all the given values in the formula to find the number of term :

$\longrightarrow{\sf{a_{n} = a + \big(n - 1\big)d}}$

$\longrightarrow{\sf{148= 4 + \big(n - 1\big)3}}$

$\longrightarrow{\sf{148= 4 + 3n - 3}}$

$\longrightarrow{\sf{148= 4 - 3+ 3n }}$

$\longrightarrow{\sf{148= 1+ 3n }}$

$\longrightarrow{\sf{3n = 148 - 1}}$

$\longrightarrow{\sf{3n = 147}}$

$\longrightarrow{\sf{n =\dfrac{147}{3}}}$

$\longrightarrow{\sf{n = \cancel{\dfrac{147}{3}}}}$

$\longrightarrow{\sf{n =49}}$

$\star{\underline{\boxed{\tt{\red{n =49}}}}}$

Hence, the number of terms is 49.

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