Question

if sum of n terms = 3n²+2n then find first term, common difference and nth term.​

Answer 1

Answer:

given sum of n terms = 3n2 + 2n

let first term be a,, second term be a, and so

if n = 1

sum = a (since there is no sum when considering only 1st term)

therefore, a = 3(1) + 2(1) = 3+ 2 = 5

then, if n = 2

S2 = a + a2 = 3(2)2 + 2(2) = 12 + 4 = 16

since a, = 5

:: a2 = 16 - 5 = 11

similarly, if n = 3

S3 = 3(3)2 + 2(3) = 27 + 6 = 33

.: a3 = 33 - (a, + a2) = 33 - 16 = 17

.. we gain that common difference = d = 17 -

11 = 11- 5 = 6

.. let nth term be an

an = a, + (n-1)d

( where a, = 5; d 6 and n n)

..an = 5 + (n-1)6

= 5 + 6n - 6

6n - 1

Answer 2

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