Question

write the expression an-ak for the AP : a,a+d,a+2d,.... hence find the common difference of the AP for which 6th term is 17 and 15th term is 67​

Answer 1

Answer:

$\huge{\pink{\green{\sf{\therefore d=\frac{50}{9}}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

▪In this question information given about two terms of an A.P.

▪So, we have to find the common difference from given information.

▪According to the given question :

$\underline \bold{given :} \\ \to a_{6} = 17 \\ \to a_{15} = 67 \\ \\ \underline \bold {to \:find : } \\ \to common \: difference(c.d) = ?$

▪From given information we make two eqn in which there is two unknown value.

▪So, after solving these two eqn we get the value of common difference.

$\to a_{6} = 17 \\ \to a + 5d = 17 - - - - - (1) \\ \\ \to a_{15} = 67 \\ \to a + 14d = 67 - - - - - (2)$

▪Subtracting eqn (1) from (2)

$\to a + 14d -( a + 5d) = 67 - 17 \\ \to a + 14d - a - 5d = 50 \\ \to 9d = 50 \\ \bold {\therefore d = \frac{50}{9} } \\ \\ put \: value \: of \: d \: in \: (1) \: to \: find \: value \: of \: a \\ \to a + 5d = 17 \\ \to a + 5 \times \frac{50}{9} = 17 \\ \to a = 17 - \frac{250}{9} \\ \bold {\to a = \frac{ - 97}{9} }$

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