Question

3) For an A.P., ifty = 6 and d= -2, then what
is the value of a ?
(A) 18
(B) 14
(C) 16 (D)20​

Answer 1

G I V E N:

• For an A.P. if $\sf{t_8}$ = 6 and d = -2, then what is the value of a?

F O R M U L A:

$\star \: {\boxed{\purple{\rm{t_n = a + (n - 1) \times d}}}}$

S O L U T I O N:

Here, we have;

• $\sf{t_8 = 6}$

• $\sf{d = -2}$

Substituting values,

$:\implies\rm{t_8 = a + (n - 1) \times d} \\ \\ :\implies\rm{6 = a + (8 - 1) \times ( - 2)} \\ \\ :\implies\rm{6 = a + 7 \times ( - 2)} \\ \\ :\implies\rm{6 = a + ( - 14)} \\ \\ :\implies\rm{6 + 14 = a} \\ \\ :\implies{\boxed{\green{\rm{a = 20}}}} \: {\red{ \star}}$

Hence,

• The value of a is 20.

Answer 2

Answer:

E N:

For an A.P. if $\sf{t_8}t$

8

= 6 and d = -2, then what is the value of a?

F O R M U L A:

$\star \: {\boxed{\purple{\rm{t_n = a + (n - 1) \times d}}}}⋆$

t n =a+(n−1)×d

S O L U T I O N:

Here, we have;

[tex[\sf{t_8 = 6}t [/tex]

8

=6

$\sf{d = -2}d=−2$

Substituting values,

$\begin{lgathered}:\implies\rm{t_8 = a + (n - 1) \times d} \\ \\ :\implies\rm{6 = a + (8 - 1) \times ( - 2)} \\ \\ :\implies\rm{6 = a + 7 \times ( - 2)} \\ \\ :\implies\rm{6 = a + ( - 14)} \\ \\ :\implies\rm{6 + 14 = a} \\ \\ :\implies{\boxed{\green{\rm{a = 20}}}} \: {\red{ \star}}\end{lgathered}$

:⟹t 8

=a+(n−1)×d

:⟹6=a+(8−1)×(−2)

:⟹6=a+7×(−2)

:⟹6=a+(−14)

:⟹6+14=a

:⟹

$\tt\bf\purple{★A=20★}$

Hence,

The value of a is 20.