Question

the sum of the 20 terms of AP is 970 and its last term is 96 find the first and common difference also write the write five terms of AP​

Answer 1

Answer:

Common difference = 5

First term = 1

Five terms are 1, 6, 11, 16, 21

Step-by-step explanation:

Let the first term be ' a '

Last term ( l ) = 96

Sum of 20 terms of AP S(20) = 96

Using Sum of n terms of AP formula

S(n) = n/2 × ( a + l )

⇒ S(20) = 20/2 × ( a + 96 )

⇒ 970 = 10 × ( a + 96 )

⇒ 97 = a + 96

⇒ 97 - 96 = a

⇒ 1 = a

Last term = a(20) = 96

⇒ a + ( n - 1 )d = 96

⇒ a + ( 20 - 1 )d = 96

⇒ a + 19d = 96

Substituting a = 1

⇒ 1 + 19d = 96

⇒ 19d = 95

⇒ d = 96 / 19 = 5

General form of AP :

a , ( a + d ), ( a + 2d ) + ( a + 3d ), ( a + 4d ) ....

• a = 1
• a + d = 1 + 5 = 6
• a + 2d = 1 + 10 = 11
• a + 3d = 1 + 15 = 16
• a + 4d = 1 + 20 = 21

Therefore we found the required answer.

Answer 2

Answer:

a=1, d=5, T1=1, T2=6, T3=11, T4=16, T5=21

Step-by-step explanation:

a+(n-1)d = 96

⇒a+(20-1)d = 96

⇒a+19d = 96

∴ a = 96-19d..........(1)

n/2{2a+(n-1)d} =970

⇒20/2{2(96-19d)+(20-1)d} = 970

⇒10(192-19d) = 970

⇒192 - 19d = 97

⇒19d = 192-97

⇒19d = 95

∴d = 5

From (1)

a = 96 - 19*5

  =96-95

∴a = 1

From Tn = a+(n-1)d,

T1=1, T2=6, T3=11, T4=16, T5=21