Question

The 3rd and 6th term of an arithmetic progression are 19 and 37 respectively. What is the 13th term?

A) 79 B) 43 C) 45 D) 49

Answer 1

Answer:

I think Answer is Option A ) is correct oneOption A is correct one i think...... . 79....

Step-by-step explanation:

Hope its help you

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• The 3rd term of an arithmetic progression is 19

$\:\:$

• The 6th term of the A.P is 37

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• It's 13th term

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

$\underline{\bold{\texttt{We know that :}}}$

$\:\:$

$\purple\longrightarrow$ $\sf a_n = a + (n - 1)d$

$\:\:$

• $\sf a_n$ = The nth term.

$\:\:$

• a = First term of AP

$\:\:$

• n = Number of term

$\:\:$

• d = common difference

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

$\underline{\bold{\texttt{3rd term is 19 :}}}$

$\:\:$

$\sf \longmapsto 19 = a + (3 - 1)d$

$\:\:$

$\sf \longmapsto 19 = a + 2d$ -------(1)

$\:\:$

Also,

$\:\:$

$\underline{\bold{\texttt{6th term is 37 :}}}$

$\:\:$

$\sf \longmapsto 37 = a + (6 - 1)d$

$\:\:$

$\sf \longmapsto 37 = a + 5d$ -------(2)

$\:\:$

$\underline{\bold{\texttt{Subtracting (1) from (2)}}}$

$\:\:$

$\sf \longmapsto 37 - 19 = a - a + 5d - 2d$

$\:\:$

$\sf \longmapsto 18 = 3d$

$\:\:$

$\sf \longmapsto d = \dfrac { 18 } { 3 }$

$\:\:$

$\bf \dashrightarrow d = 6$

$\:\:$

$\underline{\bold{\texttt{Putting d = 6 in (1)}}}$

$\:\:$

$\sf \longmapsto a + 2(6) = 19$

$\:\:$

$\sf \longmapsto a = 19 - 2(6)$

$\:\:$

$\sf \longmapsto a = 19 - 12$

$\:\:$

$\bf \dashrightarrow a = 7$

$\:\:$

$\underline{\bold{\texttt{13th term of AP is : }}}$

$\:\:$

$\purple\longrightarrow$ $\sf 7 + 12(6)$

$\:\:$

$\sf \longmapsto a_{13} = 7 + 72$

$\:\:$

$\sf \longmapsto a_{13} = 79$

$\:\:$

$\red{\bold{So \: , \: Option \: A) \: is \: correct}}$

$\rule{200}5$