A sum of ₹700 is to be used to give seven cash prizes to students of a school for their overall academic performance.

Let the value of the first prize be ₹a.

Since the value of each prize is ₹20 less than its preceding prize, so the values of the prizes are in AP with common difference −₹20.

∴ d = −₹20

Number of cash prizes to be given to the students, n = 7

Total sum of the prizes, S7 = ₹700

Using the formula, $S_{n}=\frac{n}{2}[2 a+(n-1) d]$, we get

$S_{7}=\frac{7}{2}[2 a+(7-1) \times(-20)]=700$

$\Rightarrow \frac{7}{2}(2 a-120)=700$

$\Rightarrow 7 a-420=700$

$\Rightarrow 7 a=700+420=1120$

$\Rightarrow a=160$

Thus, the value of the first prize is ₹160.

Hence, the value of each prize is ₹160, ₹140, ₹120, ₹100, ₹80, ₹60 and ₹40.