Answer: Sum of the first six terms is 2.31.
Step-by-step explanation:
Since we have given that
[tex]a_2=0.7\\\\and\\\\a_3=0.49[/tex]
Since we know the formula for "Arithmetic Progression":
[tex]a_2=a+d=0.7\implies a=0.7-d\\\\a_3=a+2d=0.49[/tex]
Now, solving the above two equations:
[tex]a+2d=0.49\\\\0.7-d+2d=0.49\\\\0.7+d=0.49\\\\d=0.49-0.70\\\\d=-0.21[/tex]
So, when we put the value of d in the first equation, we get that
[tex]a=0.7-d\\\\a=0.7+0.21\\\\a=0.91[/tex]
so, Sum of first six terms would be
[tex]S_6=\dfrac{6}{2}(2\times 0.91+(6-1)\times -0.21)\\\\S_6=3(1.82+5\times -0.21)\\\\S_6=3(1.82-1.05)\\\\S_6=2.31[/tex]
Hence, Sum of the first six terms is 2.31.
