Question

2. Find the indicated terms in each of the sequences whose nth terms are given by

Answer 1

HELLO DEAR,

( 1 ) . $\bold{a_n = \frac{n + 2}{2n + 3}}$

$\bold{a_7 = \frac{7 + 2}{14 + 3}}$

$\bold{a_7 = \frac{9}{17}}$

$\bold{a_9 = \frac{9 + 2}{18 + 3}}$

$\bold{a_9 = \frac{11}{21}}$

( 2 ). $\bold{a_n = (-1)^n2^{n + 3}(n + 1)}$

$\bold{a_5 = (-1)^5 2^{8}(6)}}$

$\bold{a_5 = (-1)(256)(6) = 1536}$

$\bold{a_8 = (-1)^82^{11}(9)}$

$\bold{a_8 = (1)(2048)(9) = 18432}$

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Solution :

i ) an = ( n+2)/( 2n+3 )

1 ) a7 = ( 7+2 )/( 2×7 + 3 )

= 9/17

2 ) if n = 9

a9 = ( 9+2 )/( 2×9 + 3 )

= 11/21

ii ) an = (-1)ⁿ×2^n+3 ×(n+1)

1) if n = 3 ,

a3 = (-1)³×2^3+3 ×(3+1)

= - 2^6 × 4

= -64×4

= -256

2) if n = 8 ,

a8 = ( -1)^8 × 2^8+3 × ( 8+1 )

= 2^11 × 9

= 18432

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