Math, asked by vikrambnair334, 5 months ago

The 10th term of an AP is 100 and 12th term is 124.Find the
common difference of the AP

Answers

Answered by sofiaaauhh
1

Answer:

12

Step-by-step explanation:

124 = 100 + (3 - 1)d

24 = 3d - d

24 = 2d

d = 12

Answered by EliteZeal
41

\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}

 \:\:

\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}

 \:\:

  • The 10th term of an AP is 100

  • The 12th term of the AP is 124

 \:\:

\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}

 \:\:

  • Common difference of the AP

 \:\:

\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}

 \:\:

We know that ,

 \:\:

 \underline{\bold{\texttt{For nth term ;}}}

 \:\:

 \sf a_n = a + (n - 1)d ⚊⚊⚊⚊ ⓵

 \:\:

Where ,

 \:\:

  •  \sf a_n = nth term

  • a = First term

  • n = Number of terms

  • d = Common difference

 \:\:

 \underline{\bold{\texttt{For 10th term :}}}

 \:\:

  •  \sf a_n = 100

  • a = a

  • n = 10

  • d = d

 \:\:

Putting the above values in ⓵

 \:\:

 \sf a_n = a + (n - 1)d

 \:\:

 \sf 100 = a + (10 - 1)d

 \:\:

➜ 100 = a + 9d ⚊⚊⚊⚊ ⓶

 \:\:

 \underline{\bold{\texttt{For 12th term :}}}

 \:\:

  •  \sf a_n = 124

  • a = a

  • n = 12

  • d = d

 \:\:

Putting the above values in ⓵

 \:\:

 \sf a_n = a + (n - 1)d

 \:\:

 \sf 124 = a + (12 - 1)d

 \:\:

➜ 124 = a + 11d ⚊⚊⚊⚊ ⓷

 \:\:

Equation ⓷ - ⓶

 \:\:

➜ 124 - 100 = a + 11d - a - 9d

 \:\:

➜ 24 = 2d

 \:\:

 \sf d = \dfrac { 24 } { 2 }

 \:\:

➨ d = 12

 \:\:

  • Hence the common difference is 12

 \:\:

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