Question

1. If the sum of first n terms of an A.P. is given by S. = 5n² + 3n, find the nth term
he nth term of the AP​

Answer 1

Step-by-step explanation:

refer to the attachment

Answer 2

Step-by-step explanation:

Here's your answer

Sn = 5n² + 3n

an = Sn - S(n-1)

= 5n² + 3n - [5(n-1)² +3(n-1)]

= 5n² +3n -[ 5(n² -2n +1)+3n -3]

= 5n² +3n - 5n² +10n -1 -3n +3

= 5n² -5n² +3n -3n +10n -1+3

an = 10n +2………..(1)

Put n= 1 in eq 1

a1= 10 ×1 +2

a1= 10 +2

a1 = 12

Put n= 2 in eq 1

a2 = 10 × 2 +2

a2 = 20 +2

a2 = 22

Common Difference (d) = a2 - a1 = 22 - 12

d = 10

Hence, the nth term ( an) = 10n +2 & the common Difference is 10.