Question

? In arithmetic sequence ( 1,7,13,19,). a) What is common difference? b) What is its ( 43) term? c) Write algebraic form? d) Is 181 a term of the sequence? e) Which term of this arithmetic sequence is ( 241 ?)

Answer 1

The given AP is 1,7,13,19

Here, a = 1;

d = 7-1 = 6

Since Last term = a + (n-1)d 

t₁₈ = 1 + (18-1)6

t_{18 = 1 + (17*6)}

t_{18 = 1 + 102}

t_{18 = 103}

_{Hope this helps!}

Answer 2

a) d= a₂-a₁ = 7-1 = 6

b) a₄₃= 1+(43-1)6 = 1+42×6 = 1+252 = 253

c) a_n = a+(n-1)d = 1+(n-1)6

d) 181= 1+(n-1)6

180=(n-1)6

n-1=30

n= 31

e) 241= 1+(n-1)6

240=(n-1)6

n-1=40

n=41

Answer 3

a) Common difference: d=a₂-a₁=7-1= 6

b) a₄₃=a+(n-1)d

=1+(43-1)(6)

=1+42×6

=1×252

=252

c)a_n=a+(n-1)d

=1+(n-1)(6)

=1+6n-6

=6n-5

d) Let 181 be n^th term of the sequence

a_n=6n-5...........(from c)

181=6n-5

186=6n

n=186/6

n=31

Hence, YES, 181 is the 31st term of the sequence

e)Let 241 be n^th term of the sequence 

a_n=6n-5

241=6n-5

6n=241+5=246

n= 246/6 =41 (integer)

Hence 241 is 41 term of the sequence

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