Math, asked by anitamarkel49, 15 days ago

which term of AP 3,8,13,18____is 148​

Answers

Answered by Ladylaurel
8

Answer :-

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

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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.

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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.

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