Question

write the expression an-ak for the AP. a, a+d, a+2d....
1) 11th term is 5 and 13th term is 79
2) a10–a5=200
3) 20th term is 10 more than the 18th term.

Answer 1

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Answer 2

Answer:

Step-by-step explanation :

an = a + ( n - 1 ) d

And , Thus

ak = a + ( k - 1 ) d

Expression of

an - ak = { a + ( n - 1 ) d } - { a + ( k - 1 ) d }

= { a + nd - d } - { a + kd + d }

= a + nd - d - a - kd - d

= nd - kd = { n - k } d

I) a11 = a + 10d = 5 {Given} ----------------- 1

And , a13 = a + 12d = 79----–---------------------- 2

By Subtracting 1 and 2 ,

d = 37

2). a10 - a5 = 200

{ a + 9d } - { a + 4d } = 200

a + 9d - a - 4d = 200

d = 40

3). a20 = 10 + a18

{Given }

a + 19d = 10 + a + 17d

2d = 10

d = 5

We only find common difference , d in three cases .

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