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
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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.
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