Question

The nth term of an A.P. is given by an = 3 + 4n. What is the

common difference of A.P.​

Answer 1

Answer:

common difference of A.P. = 4

Step-by-step explanation:

an = 3 + 4n.

a1 = 3+4 = 7

a2 = 3+4(2) = 11

a3 = 3+4(3) = 15

d = t3-t2 = t2-t1 = 15-11 = 11-7 = 4

Answer 2

$\large\underline\mathfrak\red{Given \: :- }$

• $\sf{S_n = 3 + 4n }$

$\large\underline\mathfrak\red{To \: find \: :- }$

• Common difference

$\large\underline\mathfrak\red{Solution \: :- }$

We know that,

Common difference = a2 - a1

Now,

First we find a1 then we find a2

$\sf{S_n = 3 + 4n }$

Finding a1

$\sf{a_1 = 3 + 4(1) } \\ \sf{a_1 = 3 + 4 } \: \: \: \: \: \\ \sf{a_1 = 7 } \: \: \: \: \: \: \: \: \: \: \: \:$

a1 is 7

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Finding a2

$\sf{a_2 = 3 + 4(2) } \\ \sf{a_2 = 3 + 8 } \: \: \: \: \: \: \\ \sf{a_2 = 11 } \: \: \: \: \: \: \: \: \: \: \: \:$

a2 = 11

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We know that,

$\sf{common \: difference = a_2 - a_1}$

$\sf{a_2 - a_1 } \\ \sf{11 - 7 } \: \\ \sf{4 }$

${\large{\underline{\boxed{\sf{\red{Common \: difference = 4 }}}}}}$

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