find the 31st term of an AP whose 11th term is 38 and 16th term is 73

1.	find the 31st term of an AP whose 11th term is 38 and 16th term is 73
Answer» Here a11 =38 and a16 =73Using formula a n =a +(n−1)d, to find nth term of arithmetic progression,38=a +(11−1) (d) And 73=a +(16−1)(d)⇒ 38=a +10d And 73=a +15dThese are equations consisting of two variables.We have, 38=a +10d ⇒ a =38−10dLet us put value of a in equation (73=a +15d),73=38−10d +15d ⇒ 35=5dTherefore, Common difference =d =7Putting value of d in equation 38=a +10d ,38=a +70 ⇒ a =−32Therefore, common difference = d = 7 and First term = a = -32Using formula a n =a +(n−1)d , to find nth term of arithmetic progression,a31=-32+(31−1)(7) =−32+210=178Therefore, 31st term of AP is 178.

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