Open Ended Questions `:`
(i) Write the A.P. in which a = 10 and d is any natural number.
(ii) Find the sum of the first ten terms usiing formula.
(iii) Can -80 be a term of this A.P.? Justify .

Explanation

(i) Here, a = 10 . Let d= 5.
The A.P. is 10,15,20, ….
(ii) The sum of the first ten terms.
`S_(n) = (n)/(2) [2a+ ( n-1)d]` ….(Formula)
`:. S_(10) = ( 10)/(2) [ 2 xx 10 + ( 10-1) xx 5]` …(Substituting the values )
`= 5 ( 20 + 9 xx 5)`
` = 5 xx ( 20 + 45) = 5 xx 65 = 325`.
(iii) -80 cannot be a term in this A.P.
Justification `:` Here , the values of a and d are natural numbers. So all the terms of this A.P. are natural numbers.
-80 is not a natural number.