Question

please solve question 20 step by step ​

Answer 1

Answer:

19.

given

tn= 1176

a= 3

d= 4

Now,

tn = a +( n-1 )d

1176 = 3 + (n-1)4

1176=3+ 4n-4

1176=-1 + 4n

299 = -1 + n

300= n

Step-by-step explanation:

hope it will help you.

Answer 2

||✪✪ QUESTION ✪✪||

How many terms of series 51 + 54 + 57 ____ are Required to get a sum of 810 ?

|| ✰✰ ANSWER ✰✰ ||

Here, we can see That,

→ First term = a = 51

→ common Difference = d = 54 - 51 = 3 .

→ Total terms = Let n .

→ Total sum = 810 .

we know That :-

→ sum of n terms of AP = (n/2) [ 2a + (n-1)d ]

Putting all values we get :-

→ 810 = (n/2) [ 2*51 + (n-1)3 ]

→ 1620 = n [ 102 + 3n - 3 ]

→ 1620 = 3n² + 99n

→ 3n² + 99n - 1620 = 0

→ 3(n² + 33n - 540) = 0

→ n² + 33n - 540 = 0

Splitting The middle Term now,

→ n² + 45n - 12n - 540 = 0

→ n(n + 45) - 12(n + 45) = 0

→ (n + 45)( n - 12) = 0

Putting both Equal to Zero now,

→ (n + 45) = 0

→ n = (-45)

Or,

→ ( n - 12) = 0

→ n = 12

Since, Negative value not possible.

Hence, Required Number of Terms Required To get a sum of 810 of given Series is 12.