Question

If 6th term of an ap. Is -10 and it's 10 term is -26,then find first term and difference

Answer 1

here is your answer bro hope it helps!!!

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• 6th term of an ap is -10

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• 10 th term is -26

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$\red{\underline \bold{To \: Find:}}$

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• First term and common difference

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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$\underline{\bold{\texttt{We know that :}}}$

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$\purple\longrightarrow$ $\bf a_n = a + (n - 1)d$

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Below are the each term used above

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• $\rm a_n$ = nth term

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• a = First term

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• n = Number of term

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• d = Common difference

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We are given that the 6th term of is -10

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So,

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$\sf \longmapsto -10 = a + (6 - 1)d$

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$\bf \dashrightarrow a + 5d = -10$ -----(1)

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Also,

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10 th term is -26

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So,

$\sf \longmapsto -26 = a + (10 - 1)d$

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$\sf \longmapsto -26 = a + 9d$

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$\bf \dashrightarrow -a - 9d = 26$ -------(2)

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$\underline{\bold{\texttt{Adding (1) \& (2)}}}$

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$\sf \longmapsto a + 5d - a - 9d = -10 + 26$

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$\sf \longmapsto -4d = 16$

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$\sf \longmapsto d = \dfrac { 16 } { -4 }$

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$\bf \dashrightarrow d = -4$

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$\underline{\bold{\texttt{Putting d = -4 in (1)}}}$

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$\sf \longmapsto a + 5(-4)= -10$

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$\sf \longmapsto a - 20 = -10$

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$\sf \longmapsto a = -10 + 20$

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$\bf \dashrightarrow a = 10$

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Hence First term is 10 & common difference is -4

$\rule{200}5$