The nth term of an A.P is 4n+2. The common difference will be * urgent plzz asap
Answers
Answer:
\huge\underline\mathfrak\blue{Answer-}
Answer−
Common difference (d) = 4
\huge\underline\mathfrak\blue{Explanation-}
Explanation−
Given :
\bold{a_n}a
n
= 3 + 4n
To find :
Common difference (d)
Solution :
It is given that,
\bold{a_n}a
n
= 3 + 4n_____(1)
Now,
put n = 1, 2, 3 turn wise. So that we can find \bold{a_1}a
1
, \bold{a_2}a
2
and \bold{a_3}a
3
.
______________
★For finding \bold{a_1}a
1
,
put n = 1 in (1)
a_1a
1
= 3 + 4 (1)
\implies⟹ a_1a
1
= 3 + 4
\implies⟹ a_1a
1
= 7
_______________
★For finding \bold{a_2}a
2
,
put n = 2 in (1).
a_2a
2
= 3 + 4 (2)
\implies⟹ a_2a
2
= 3 + 8
\implies⟹ a_2a
2
= 11
_______________
★For finding \bold{a_3}a
3
,
put n = 3 in (1).
a_3a
3
= 3 + 4 (3)
\implies⟹ a_3a
3
= 3 + 12
\implies⟹ a_3a
3
= 15
________________
So, the AP will be :
\implies⟹ 7, 11, 15 .........
Here, $$a_1}$$ = 7
$$a_2$$ = 11
$$a_3$$ = 15
Now,
common difference (d) = $$a_2$$ - $$a_1}$$
$$\implies$$ common difference (d) = 11 - 7
$$\implies$$ common difference (d) = 4
Similarly,
common difference (d) = $$a_3$$ - $$a_2$$
$$\implies$$ common difference (d) = 15 - 11
$$\implies$$ common difference (d) = 4
Hence, the common difference (d) is 4.
__________________
*Note - If the same question is in 1 mark, then you can give answer as the coefficient of n i.e 4.
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