Question

Ginen a=2 d=8, Sn=90, find n, an and s50​

Answer 1

Answer:

n = 5

a(n) = 34

S(50) = 9900

Step-by-step explanation:

Sum of n terms in an A.P is given by,

$\sf S_n = \dfrac{n}{2}[2a+(n-1)d]$

Substituting the given values,

90 = n/2 [2(2) + (n – 1)(8)]

90 × 2 = n(4 + (n – 1)(8)]

180 = n (4 + 8n – 8)

180 = n (8n – 4)

180 = 8n² – 4n

8n² – 4n – 180 = 0

4(2n² – n – 45) = 0

2n² – n – 45 = 0

2n² – 10n + 9n – 45 = 0

2n(n – 5) + 9(n – 5) = 0

(n – 5) (2n + 9) = 0

=> n - 5 = 0 ; n = +5

=> 2n + 9 = 0 ; n = –9/2

n can't be negative. So n = 5

______________________

nth term :

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

Substituting,

$\sf a_n = 2 + (5-1)(8) \\ \sf a_n = 2+4(8) \\ \sf a_n = 2+32 \\ \sf a_n = 34$

______________________

Value of S(50) :

S(50) = 50/2 [ 2(2) + (50 – 1)(8) ]

S(50) = 25 [ 4 + 49(8) ]

S(50) = 25 [ 4 + 392 ]

S(50) = 25 [ 396 ]

S(50) = 9900

Answer 2

Answer:

a=2,d=8,s

n

=90

s

n

=

2

n

[2a+(n−1)d]

90=

2

n

[4+(n−1)8]

180=n[8n−4]

180=8n

2

−4n

=8n

2

−4n−180=0

=2n

2

−n−45=0

=2n

2

−10n+9n−45=0

=2n(n−5)−9(n−5)

=(2n−9)(n−5)

n=5

a

n

=a+(n−1)d

a

n

=2+(5−1)8

a

n

=2+32

a

n

=34