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  • If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term? (A) 30 (B) 33 (C) 37 (D) 38

If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?

(A) 30

(B) 33

(C) 37

(D) 38

Answers (1)

We know that

\\a\textsubscript{n }= \textsubscript{ }a + ( n - 1 ).d $ \ldots $ ..(1)\\ $Given a\textsubscript{2} $= 13\\ a\textsubscript{5} = 25\\ a + d = 13 $ \ldots $ \ (2)\ \ \ \ ($Put n$ = 2 $in eq. (1) )$\\ a + 4d = 25 $ \ldots $ \ (3)\ \ \ \ \ ($Put n = 5 in eq. (1) )$\\ \ $Subtract eq. (1) and (2)\\$ - 3d = - 12\\ \ \ \ \ d = \frac{12}{3} \\ \ \ \ d = 4\\ $Put d= 4 in equation (2)\\ $ a + 4 = 13\\ a = 13 - 4\\ a = 9\\ a\textsubscript{7}\ =\ a\ +\ (7\ -\ 1).d\ \ \ \ (Put n = 7 in eq. (1) )\\ \ \ = 9 + (6). (4)\\ \ = 9 + 24\\ = 33\\

Hence option B is correct.

Posted by

infoexpert21

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