Question

sum of the first n terms of an arithmetic progression is 5n²-3n find the arithmetic progression and also its 16th term
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Answer 1

Answer:

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Answer 2

Answer:

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Let an denotes the nth terms and Sn denotes the sum of the first n terms of given AP.

Given:

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.