39.5k views
3 votes
Question In an AP the 2nd and 6th term are 11 and -17 respectively. Find of The 1st Term тет b) The common citterence c) The Sum of the 1st 50 term.



1 Answer

3 votes
To find the first term of the arithmetic progression (AP), we can use the formula:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

Given that the 2nd term is 11, we can substitute these values into the formula:

11 = a1 + (2-1)d
11 = a1 + d

Similarly, given that the 6th term is -17, we can substitute these values into the formula:

-17 = a1 + (6-1)d
-17 = a1 + 5d

Now we have a system of two equations:

11 = a1 + d
-17 = a1 + 5d

We can solve this system of equations to find the values of a1 and d.

Subtracting the first equation from the second equation, we get:

-17 - 11 = (a1 + 5d) - (a1 + d)
-28 = 4d

Dividing both sides by 4, we get:

d = -7

Substituting this value of d into the first equation, we can solve for a1:

11 = a1 + (-7)
11 = a1 - 7
a1 = 11 + 7
a1 = 18

So, the first term of the AP is 18.

b) The common difference is -7.

c) To find the sum of the first 50 terms, we can use the formula for the sum of an arithmetic series:

Sn = (n/2)(2a1 + (n-1)d)

Substituting the values, we get:

S50 = (50/2)(2(18) + (50-1)(-7))
S50 = 25(36 + 49(-7))
S50 = 25(36 - 343)
S50 = 25(-307)
S50 = -7675

So, the sum of the first 50 terms is -7675.
User Swabygw
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.