Find the $7^{t h}$ term from the end of the Arithmetic Progression $7, 10, 13, . . . . . . . .184$ .

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Solution

Given an $A P$
$7, 10, 13, . . . . . 184$
For finding $7^{t h}$ term from the last we have
First term = $184$
Common difference $= 7 - 10 = - 3$
Now
$a_{7} = a + (7 - 1) d = a + 6 d$
$a_{7} = 184 + 6 \times - 3$
$a_{7} = 184 - 18$
$a_{7} = 166$
hence $7^{t h}$ term from the last is $166$

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