Question

If the $j^{th}$ term and $k^{th}$ term of an A.P. are k and j respectively, the ( k + j) th term is:?

• A. 0
• B. 1
• C. k + j + 1
• D. k + j - 1

Answer 1

Answer: (A)

0

Answer 2

Let a, be the first term and d, the common difference. General term ($n_{th}$ term) of the AP is $T_n = a + (n - 1) d$ As given, $T_j = a + (j - 1) d = k$ ....(1) $T_k = a + (k - 1) d = j$ ....(2) Subtracting (2) from (1) we get $(j - k) d = k - j \, \Rightarrow d = - 1$ On putting d = - 1 in (1), we get a + (j - 1) (- 1) = k $\Rightarrow$ a = k + j - 1 Now, $T_{k + j}$ = a + (k + j - 1)d = k + j - 1 + (k + j) -1 = (k + j - 1) - (k + j - 1) = 0