Question

4. Find five consecutive terms of an A.P. whose sum is 100 and the ratio of the
first to the last term is 2:3.​

Answer 1

Answer:

Step-by-step explanation:

LET THE CONSECUTIVE TERMS OF AP BE IN THE FORM

a  - 2d ,  a - d ,  a  ,  a + d ,  a + 2d

THUS BY GIVEN CONDITIONS

a - 2d + a - d + a  + a+d + a + 2d = 100

5a = 100

thus a = 20

ALSO

$\frac{a - 2d }{a +2d }$   =  $\frac{2}{3}$

3a - 6d =  2a + 4d

a = 10d

but a = 20

thus d = 2

HENCE THE FIVE CONSECUTIVE TERMS OF AP ARE

16  ,  18  ,  20  ,  22  ,  24