Answer:
740
Step-by-step explanation:
Let the AP be a, a+d, a+2d, a+3d, ...
The term of AP is given by:
[tex]t n =a+(n-1)d[/tex]
We are given that the third term is 7.
[tex]t 3=7[/tex]
⇒ [tex]a+(3-1)d=7[/tex]
⇒[tex]a+2d=7 ---(1)[/tex]
Also, the seventh term is 2 more than three times the third term.
[tex]t7=3t3+2[/tex]
⇒[tex]a+ (7-1)d=3(a+(3-1)d)+2[/tex]
⇒[tex]a+6d=3(a+2d)+2[/tex]
⇒[tex]a+6d=3a+6d+2[/tex]
⇒[tex]-2a=2[/tex]
⇒[tex]a=-1[/tex]
We can put it in (1)
[tex]a+2d=7[/tex]
⇒[tex](-1)+2d=7[/tex]
⇒[tex]2d=8[/tex]
⇒d=4
Now, the Sum of n terms of an AP is given by the formula:
[tex]sn=\frac{n}{2}(2a+(n-1)d)[/tex]
So, Sum of first 20 terms would be:
[tex]s 20=\frac{20}{2}(2(-1) +(20-1) x 4)[/tex]
⇒[tex]s20=10(-2+19 x 4)[/tex]
⇒[tex]s 20=10 x(-2+76)[/tex]
⇒[tex]s 20= 10 x 74[/tex]
⇒[tex]s 20=740[/tex]
Thus, The Sum of first 20 terms of the AP is 740.
