Question

An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 26th term.

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Answer 1

Answer:

58

Step-by-step explanation:

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Answer 2

$\huge{\bf{\green{\mathfrak{Question:-}}}}$

• An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 26th term.

$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

• $\sf{We\: know \:that,\: a_{3} \:=\: 12.}$

• $\textsf{a + 2d = 12. ———⟩ \boxed{1}}$

• $\textsf{A.P contains 50 terms.}$

• $\textsf{Last term = 106.}$

• $\sf{This\: means\: that,\: a_{50}\: =\: 106.}$

• $\textsf{a + 49d = 106. ———⟩ \boxed{2}}$

• $\textsf{\boxed{2} - \boxed{1},}$

• $\textsf{a + 49d = 106}$
• $\textsf{- (a + 2d = 12)}$

• $\textsf{a + 49d = 106}$
• $\textsf{- a - 2d = - 12}$
• ———————
• $\textsf{47d = 94}$

• $\sf d \: = \: \dfrac{94}{47}$

• $\boxed{\sf d \: = \: 2.}$

• $\textsf{Substituting d = 2 in \boxed{1},}$

• $\sf a \:+\: 2\:*\:2 \:= \:12$

• $\sf a\:+\: 4 \:=\:12$

• $\sf a \: = \: 12 \: - \: 4$

• $\boxed{\sf a \: = \: 8.}$

• $\sf{Now,\: a_{26} \:=\: ?}$

• $\sf a \: + \: 25d$

• $\sf 8 \: + \: 25 \: * \: 2$

• $\sf 8 \: + \: 50$

• $\boxed{\sf a_{26} \: = \: 58.}$

$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

• $\boxed{\therefore{\sf a_{26} \: = \: 58.}}$