If for an $A . P$ , $d = 11$ , what is $t_{17} - t_{15}$ ?

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Solution

Given that,
Common difference $= d = 11$
first term $= a = a$
number of the term $= n$
$\begin{matrix} T_{n} = a + (n - 1) d T_{17} = a + (17 - 1) 11 \end{matrix}$
$= a + (16) 11$
$= a + 176$
$\begin{matrix} T_{n} = a + (n - 1) d T_{15} = a + (15 - 1) 11 \end{matrix}$
$= a + (14) 11$
$= a + 154$
then,
$T_{17} - T_{15} = (a + 176) - (a + 154)$
$= a + 176 - a - 154$
$= 22$
Thus,
We get $A . P = 22$

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