Question

Pls solve atep by step. Its very urgent .No spams plzzzz.​

Answer 1

Answer:

sum of an AP is given by n/2 (2a + ( n-1) d)

since sum of first 5 term is given

so,

5/2(2a+4d) = 25/2

= a +2d =5/2--------(1)

and a/d = 2/3-----------(2)

so, I it value of a form (2) in (1)

= 2d/3+2d=5/2

so,

d=15/16 and a= 2d/3= 5/8

there fore first five numbers are

5/8, 25/10, 40/10 , 55/10, 70/10

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Answer 2

SoluTion :-

Sum of an AP is given by

$\boxed {\rm {S_{n}=\frac{n}{2}(2a+(n-1)d) }}$

Sum of first 5 terms

$\rm {S_{5}=\frac{5}{2}(2a+(5-1)d)}\\\\\\\rm {\frac{25}{2} =\frac{5}{2}(2a+4d) }\\\\\\\rm {a+2d=\frac{5}{2} \ ...(1) }$

Now,

$\tt {\frac{a}{d} =\frac{2}{3}}\\\\\\\tt {a=\frac{2d}{3} \ ...(2)}$

Putting together,

$\sf {\frac{2d}{3} +2d=\frac{5}{2}}\\\\\\\sf {\frac{2d+6d}{3} =\frac{5}{2}}\\\\\\\sf {4d+12d=15}\\\\\\\sf {d=\frac{15}{16} }$

Thus,

$\tt {a=\frac{2d}{3}}\\\\\\\tt {\frac{2}{3} \times \frac{15}{6} =\frac{5}8} }$

First five terms of an AP are a, a+d, a+2d, a+3d, a+4d

$\rm {\Rightarrow \frac{5}{8} ,\frac{25}{16} ,\frac{40}{16} ,\frac{55}{16} ,\frac{70}{16} }$