Question

if s7 = 700 and Ap x, x-20, x-40 .. find value of x=? ​

Answer 1

Answer:

Step-by-step explanation:

▶ Solution :-

→ Let the first term prize be x.

•°• a = x.

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

•°• d = - ₹ 20.

→ Number of cash prizes to be given to the students , •°• n = 7.

→ Then, the value of these prizes be ₹x , ₹( x - 20 ), ₹( x - 40 ), ...... and ₹( x - 120 ) respectively.

→ Total sum of the prizes , •°• S\tiny 77 = ₹700 .

▶ Now,

→ Using Identity :-

°•° S\tiny nn = n/2 [ 2a + ( n - 1 )d ] .

=> S\tiny 77 = 7/2 [ 2x + ( 7 - 1 ) (-20) ] .

=> 700 = 7/2 [ 2x + ( 6 × (-20) ) ] .

=> 700 = 7/2 [ 2x - 120 ] .

=> 700 = (7 × 2 )/2 [ x - 60 ] .

=> 7x - 420 = 700 .

=> 7x = 700 + 420 .

=> 7x = 1120 .

=> x = 1120/7 .

•°• x = 160 .