If 7 th term of AP is 34 and 13th term is 64 then its 18th term is :

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Solution

The correct option is D 89
Given, 7th term = 34 and 13th term = 64.
$a + 6 d = 34 a + 12 d = 64$ .
From the above two equations, we can deduce, 'd' = 5.
$- 6 d = - 30 ⟹ d = 5$ . [subtracting both equations]
Substituting 'd' = 5 in either equation, will give 'a'.
$a + 6 d = 34 ⟹ a + 6 (5) = 34 ⟹ a + 30 = 34 o r a = 4$ .
First term 'a' = 4.
$t_{18} = a + 17 d ⟹ t_{18} = 4 + 17 (5) ⟹ t_{18} = 89$ .
18th term of the sequence = 89.

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