Write the expression $a_{n} - a_{k}$ for the A.P. a, a+d, a+2d,...
Hence, find the common difference of the A.P. for which
(i) 11th term is 5 and 13th term is 79.
(ii) $a_{10} - a_{5} = 200$
(iii) 20th term is 10 more than the 18th term.

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Write the expression an−ak for the A.P: a+d, a+2d.... and find the common difference of the AP for which (i) 11th terms is 5 and 13th terms is 79.(ii) 20th term is 10 more then the 18th term.

an=a+ndak=a+kdan−ak=(n−k)d(i) 5=a+11d79=a+13dSolving above 2 equations74=2d⇒d=37(ii) a20−a18=10⇒(20−18)d=10⇒d=5

Write the expression $a_{n} - a_{k}$ for the A.P: a+d, a+2d.... and find the common difference of the AP for which
(i) 11th terms is 5 and 13th terms is 79.
(ii) 20th term is 10 more then the 18th term.

$a_{n} = a + n d a_{k} = a + k d$

$a_{n} - a_{k} = (n - k) d$

(i) $5 = a + 11 d 79 = a + 13 d$

Solving above 2 equations
$74 = 2 d \Rightarrow d = 37$

(ii) $a_{20} - a_{18} = 10 \Rightarrow (20 - 18) d = 10 \Rightarrow d = 5$