Question

the algebraic expression of an arithmetic sequence is 4n+3 find its
a,first term and common difference
b,eleventh term
c,check whether 100 is a term of the series
d,check whether 2020 difference of any 2 term?why?​

Answer 1

Answer:

a) xn=a+(n-1)d

=dn+a-d

4n+3 is in the form dn+a-d

here, d=4 and a-d=3=a-4=3 = a=3+4=7

so a=7 and commondifference=4

b)4n+3 is the algebraic expression

X11=4×11+3=44+3=47

c)if a no be a term,difference of any two terms should be the multiple of commondifference.

so, X100-X11 will be the multiple of d=4

since,4n+3 is the expression,X100=4×100+3=403.

let the multiple of commondifference be X.

i.e X100-X11=403-47=4 × X

X=356/4=89

so 100 is a term in the series.

d) a number be the difference of any 2 terms,

it must be the multiple of commondifference.

2020/4=505

so 2020 can the difference of 2 terms.