Math, asked by nikhithamanitha28, 1 day ago

The sum of the first 11 terms of an arithmetic sequence is 220.

a) Find the 6^ =n term.

b) Find the sum of the 5^ prime h and 7^ \# terms.

c) Find the sum of the 1 ^ 51 and the 11^ iff terms.​

Answers

Answered by pulakmath007
1

SOLUTION

CORRECT QUESTION

The sum of the first 11 terms of an arithmetic sequence is 220.

a) Find the 6th term.

b) Find the sum of the 5th and 7th term

c) Find the sum of the 1st and the 11th term

FORMULA TO BE IMPLEMENTED

If in an arithmetic progression

First term = a

Common difference = d

1. nth term of the AP = a + ( n - 1 )d

2. Sum of first n terms of an arithmetic progression

  \displaystyle \sf =  \frac{n}{2}  \bigg[2a + (n - 1)d  \bigg]

EVALUATION

Let First term = a and Common difference = d

Here it is given that sum of the first 11 terms is 220

Thus we have

 \displaystyle \sf \frac{11}{2}  \bigg[(2 \times a) + (11 - 1)d  \bigg] = 220

 \displaystyle \sf  \implies 2a+10d = 40 \:  \:  \:  \:

 \displaystyle \sf  \implies a+5d = 20 \:  \:  \:  \:  -  -  - (1)

a) The 6th term of the AP

 \displaystyle \sf   =  a+(6 - 1)d

 \displaystyle \sf   =  a+5d

 \displaystyle \bf   = 20

b) 5th term of the AP

= a + ( 5 - 1)d

= a + 4d

7th term of the AP

= a + ( 7 - 1)d

= a + 6d

Hence the required sum

= a + 4d + a + 6d

= 2a + 10d

 \sf = 2(a + 5d)

 \sf = 2 \times 20

 \bf = 40

c) 1st term = a

11th term of the AP

= a + ( 11 - 1)d

= a + 10d

Hence the required sum

= a + a + 10d

= 2a + 10d

 \sf = 2(a + 5d)

 \sf = 2 \times 20

 \bf =40

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