The mean of the series $a,a + nd,\,\,a + 2nd$ is
The mean of the series $a,a + nd,\,\,a + 2nd$ is
- A
$a + (n - 1)\,d$
- B
$a + nd$
- C
$a + (n + 1)\,d$
- D
None of these
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Let $AP ( a ; d )$ denote the set of all the terms of an infinite arithmetic progression with first term a and common difference $d >0$. If $\operatorname{AP}(1 ; 3) \cap \operatorname{AP}(2 ; 5) \cap \operatorname{AP}(3 ; 7)=\operatorname{AP}( a ; d )$ then $a + d$ equals. . . . .
Let $AP ( a ; d )$ denote the set of all the terms of an infinite arithmetic progression with first term a and common difference $d >0$. If $\operatorname{AP}(1 ; 3) \cap \operatorname{AP}(2 ; 5) \cap \operatorname{AP}(3 ; 7)=\operatorname{AP}( a ; d )$ then $a + d$ equals. . . . .
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