Question

`The first term of the AP is 19. The ratio of its 6th term to the 22nd term is 11:31. How to calculate the value of a6​

Answer 1

Answer:

hey here is your solution

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so here we go

Step-by-step explanation:

here let the sixth term of an ap be a+5d and its 22nd term be a+21d

so here a=19

thus according to the given condition

a+5d/a+21d=11/31

so 31(a+5d)=(a+21d)×11

thus substitute value of a in it

you get 31×(19+5d)=11×(19+21d)

solve it you get

589+155d=231d+209

ie 380=76d

so d=5

now to find a6 ie t6 i.e. 6th term

apply tn=a+(n-)×d formula

put n=6 and respecteted values in it

you get t6=44

hence the 6th term is 44

verify the answer by substituting given and found values in (1)