Question

2k +1, 13,5k-3 are three consecutive terms of an ap then k=____​

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

Answer is (B) 4

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Explanation :

If 2k + 1 , 13 , 5k - 3 are in A.P then,

$\large{\boxed{\sf{b \: = \: \dfrac{a \: + \: c}{2}}}} \\ \\ \implies {\sf{13 \: = \: \dfrac{2k \: + \: 1 \: + \: 5k \: - \: 3}{2}}} \\ \\ \implies {\sf{13 \: \times \: 2 \: = \: 7k \: - \: 2}} \\ \\ \implies {\sf{26 \: = \: 7k \: - \: 2}} \\ \\ \implies {\sf{7k \: = \: 26 \: + \: 2}} \\ \\ \implies {\sf{7k \: = \: 28}} \\ \\ \implies {\sf{k \: = \: \dfrac{28}{7}}} \\ \\ \implies {\sf{k \: = \: 4}} \\ \\ {\boxed{\sf{Value \: of \: k \: is \: 4}}}$

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt Given\begin{cases} \sf{2k + 1, \: 13, \: 5k - 3 \: are \: three \: consecutive \: terms \: of \: A.P}\end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to fund the value of k.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

We know the formula to find value of k. As, they are three consecutive numbers

$\Large{\star{\boxed{\rm{b = \frac{a + c}{2}}}}}$

__________________[Put Values]

$\tt{\mapsto 13 = \frac{2k + 1 + 5k - 3}{2}} \\ \\ \tt{\mapsto 13 = 13 \times 2 = 7k - 2} \\ \\ \tt{\mapsto 26 + 2 = 7k} \\ \\ \tt{\mapsto k = \frac{\cancel{28}}{\cancel{7}}} \\ \\ \tt{\mapsto k = 4}$

$\tt{\therefore \: Option \: B \: is \: correct.}$