Question

The 6th term of an ap is -10 and 10 th term is-26 determine the 15th term of AP

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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

$\:\:$

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

$\:\:$

• 6th term of an ap is -10

$\:\:$

• 10 th term is -26

$\:\:$

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

$\:\:$

• The 15th term of AP

$\:\:$

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

$\:\:$

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

$\:\:$

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

$\:\:$

Below are the each term used above

$\:\:$

• $\rm a_n$ = nth term

$\:\:$

• a = First term

$\:\:$

• n = Number of term

$\:\:$

• d = Common difference

$\:\:$

We are given that the 6th term of is -10

$\:\:$

So,

$\:\:$

$\sf \longmapsto -10 = a + (6 - 1)d$

$\:\:$

$\bf \dashrightarrow a + 5d = -10$ -----(1)

$\:\:$

Also,

$\:\:$

10 th term is -26

10 th term is -26 $\:\:$

So,

$\sf \longmapsto -26 = a + (10 - 1)d$

$\:\:$

$\sf \longmapsto -26 = a + 9d$

$\:\:$

$\bf \dashrightarrow -a - 9d = 26$ -------(2)

$\:\:$

$\underline{\bold{\texttt{Adding (1) \& (2)}}}$

$\:\:$

$\sf \longmapsto a + 5d - a - 9d = -10 + 26$

$\:\:$

$\sf \longmapsto -4d = 16$

$\:\:$

$\sf \longmapsto d = \dfrac { 16 } { -4 }$

$\:\:$

$\bf \dashrightarrow d = -4$

$\:\:$

$\underline{\bold{\texttt{Putting d = -4 in (1)}}}$

$\:\:$

$\sf \longmapsto a + 5(-4)= -10$

$\:\:$

$\sf \longmapsto a - 20 = -10$

$\:\:$

$\sf \longmapsto a = -10 + 20$

$\:\:$

$\bf \dashrightarrow a = 10$

$\:\:$

$\underline{\bold{\texttt{The 15th term}}}$

$\:\:$

$\purple\longrightarrow$ $\rm a_{15} = 10 + (15 - 1)-4$

$\:\:$

$\sf \longmapsto a_{15} = 10 + 14 \times -4$

$\:\:$

$\sf \longmapsto a_{15} = 10 - 56$

$\:\:$

$\bf \dag \: \: a_{15} = -46$

$\:\:$

Hence 15th term of this AP is -46

$\rule{200}5$