Question

the first term of an ap of consecutive integer is p^2+1 . The sumof (2p+1)terms of this series can be expressed as​

Answer 1

Answer: 2p³+3p²+3p+1

Step-by-step expl - given that the  1st  term is p²+ 1

⇒ a = p² +1

also .. the terms of ap are consecutive

⇒ d = 1

n = 2p +1        ( given)

now . by using formula   Sn =  n/ 2  [ 2a + (n-1) d ]

⇒ 2p+1 /2  [ 2 (p² +1 ) = ( 2p+1-1) 1]

⇒2p+1/2  [2p²+2 + 2p]

⇒2p +1/2    ×  2 ( p²+1+p)

⇒ 2p+1 ( p² +1+p)

⇒2p³ +2p +2p² + p²+1+p

⇒2p³ + 3p²+3p +1