Question

can the sum of 'n' term in an AP is nsquare + 13 n justify you answer​

Answer 1

yes, sum of n terms of an AP would be n² + 13n

whose first term is 14 and common difference is 2.

we have to check sum of n terms in an AP would be n² + 13n or not .

let's try to resolve it in standard form of formula of sum of n terms.

i.e., Sn = n/2[2a + (n - 1)d ] .......(1)

n² + 13n = n(n + 13)

= n/2 (2n + 26)

= n/2 [2n - 2 + 28 ]

= n/2 [ 2(n - 1) + 2 × 14 ]

= n/2 [2(14) + (n - 1)2 ]........(2)

on comparing equations (1) and (2) we see a = 14 and d = 2 {a and d are both integers }

hence sum of n terms of an AP would be n² + 13n

whose first term is 14 and common difference is 2.

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Answer 2

$\huge\bold\purple{Answer:-}$

we have to check sum of n terms in an AP would be n² + 13n or not .

let's try to resolve it in standard form of formula of sum of n terms.

i.e., Sn = n/2[2a + (n - 1)d ] .......(1)

n² + 13n = n(n + 13)

= n/2 (2n + 26)

= n/2 [2n - 2 + 28 ]

= n/2 [ 2(n - 1) + 2 × 14 ]

= n/2 [2(14) + (n - 1)2 ]........(2)

on comparing equations (1) and (2) we see a = 14 and d = 2 {a and d are both integers }

hence sum of n terms of an AP would be n² + 13n

whose first term is 14 and common difference is 2.