Question

sum of 1st 15 terms of an arithmetic sequence is 525 its 12th term is 51 (a) find its 8th term (b) find the 1st term ​

Answer 1

$\bf\huge\underline{\underline{ Given :- }}$

• sum of 1st 15 terms of an AP is 525
• 12th term is 51

$\bf\huge\underline{\underline{ To \: Find:- }}$

• 8th term
• 1st term

$\bf\huge\underline{\underline{ Formula \: Used }}$

• $\boxed{\bf middle \: term = \frac{sum}{ no. \: of \: terms }}$

• $\boxed{\bf d = \frac{ x_{n} - x_{m} }{n- m} }$

$\bf\huge\underline{\underline{ Answer :- }}$

$\bf\large\underline{\underline{ 8^{th} term }}$

• $\boxed{\bf middle \: term = \frac{sum}{ no. \: of \: terms }}$

• $x_{8} = \frac{525}{15}$

• $x_{8}= 35$

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8th term = 35

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$\bf\large\underline{\underline{ 1^{st} term }}$

• $\boxed{\bf d = \frac{ x_{n} - x_{m} }{n- m} }$

• common difference = $\bf d = \frac{51 - 35}{12 - 8 }$

• common difference = $\bf \frac{16}{4}$

• common difference = $\bf 4$

• $\bf x_{8} = 35$

• $\bf x _{1} = 35 - 7d$

• $\bf x_ {1 } = 35 - 28$

• $\bf x_ {1 } = 7$

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1st term = 7

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