Question

which term of AP 3,8,13,18____is 148​

Answer 1

Answer :-

148 is the 28th term of A.P. 3, 8, 13, 18 .. .. ..

Step-by-step explanation:

To Find :-

• Which term of A.P. 3, 8, 13, 18 .... ... is 148.

★ Solution

Given that,

Arithmetic progression [A.P.] = 3, 8, 13, 18 .. .. ..

Finding the first term, and common difference :-

First term (a) = 3.

Common difference :-

→ 8 - 3 = 5

→ 13 - 8 = 5

→ 18 - 13 = 5

Hence, The common difference is 5.

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We know,

$\purple{ \bigstar} \: \boxed{\sf{{t}_{n} = a + (n - 1)d}}$

Where,

• $\sf{{t}_{n}}$ = nth term
• a = first term
• n = number of terms.
• d = common difference.

According the question,

$\sf{ \longrightarrow \: \: \: \: {t}_{n} = a + (n - 1)d}$

$\sf{ \longrightarrow \: \: \: \: 148 = 3 + (n - 1)5}$

$\sf{ \longrightarrow \: \: \: \: 148 - 3 = (n - 1)5}$

$\sf{ \longrightarrow \: \: \: \: 145 = (n - 1)5}$

$\sf{ \longrightarrow \: \: \: \: \dfrac{145}{5} = (n - 1)}$

$\sf{ \longrightarrow \: \: \: \: \cancel{\dfrac{145}{5}} = (n - 1)}$

$\sf{ \longrightarrow \: \: \: \: 29 = (n - 1)}$

$\sf{ \longrightarrow \: \: \: \: (n - 1) = 29}$

$\sf{ \longrightarrow \: \: \: \: n = 29 - 1}$

$\sf{ \longrightarrow \: \: \: \: n = 28}$

Hence,

148 is the 28th term.