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in an ap the first term is 1, if second term, tenth term and thirty-fourth terms forms a GP, then what is the fourth term of the GP series?
t1 = 1t2 = 1+dt10 = 1 + 9dt34 = 1 + 33dthese are all in G.P. then,t2/t1 = t34/t10solve for d and thewrite t4 = 1 + 3d thus.
here, a1=1 and 2,10,34 are forming gp. so we can write a2= a+d, a10= a+9d, and a34= a+33d. now its given that they are forming gp so by property we can write,(a+9d)square= (a+d)(a+33d). (a=1)on solving we get d=1/3.so 4th term will be = a+3d= 2.
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