for what values of 'a' does 5^1+x+5^1-x, a/2, 25^x+25^-x form three consecutive terms of an A P - Maths - Sequences and Series

Question

for what values of 'a' does 5^1+x+5^1-x, a/2, 25^x+25^-x form three
consecutive terms of an A P

Neha Sethi · Accepted Answer

Dear student
Since, 51+x+51-x,a2,25x+25-x are in APSo, 2×a2=51+x+51-x+25x+25-x  when x,y,z are in AP⇒2y=x+za=51+x+51-x+25x+25-xNow put 5x=t so that t>0, we can havea=5t+5t+t2+1t2a=t2+1t2+5t+1ta=t-1t2+2+5t-1t2+2a=t-1t2+5t-1t2+12a≥12Thus values of a are given by inequality a≥12
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for what values of 'a' does 5^1+x+5^1-x, a/2, 25^x+25^-x form three consecutive terms of an A.P