Question

consider an arithmetic sequence with common difference 20.if the sum of reciprocals of two consecutive terms of the sequence is 1/24.find the first term of the sequence? ​

Answer 1

Answer:

Let a and d are first term and common difference of an ap respectively

let a and a+d the two consecutive terms of a given AP.

now according to question

1/a+1/a+d=1/24

a+d+a/a(a+d) =1/24

2a+20/a2+20a=1/24

a2+20a=48a+480

a2-28a-480=0

a2-40a +12a-480=0

a(a-40)+12(a-40)=0

(a-40)(a+12)=0

a-40=0,a+12=0

a=40,a=-12 is rejected

so, first term of an ap is 40