Question

The sum of first m terms an A.P 4m²- m then find its nth term
Also find the 21st term
this A.P

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Answer 1

Step-by-step explanation:

Sn = 4m²-m

a1 = S1 = 4(1)²-(1) = 3

a2 = S2-S1 = 4(2)²-2-3 = 16-5 = 11

d = a2-a1 = 11-3 = 8

nth term is 107 (given)

Tn = 107

a1+(n-1)d = 107

3+(n-1)8 = 107

n-1 = 104/8 = 13

=> n = 14

Now,

20th term

T20 = a1+19d

= 3+19×8 = 3 + 152 = 155

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Answer 2

$Sn = 4m²-m\\\\a1 = S1 \\= 4(1)²-(1) \\= 3\\\\a2 = S2-S1 \\= 4(2)²-2-3 \\= 16-5 \\= 11\\\d = a2-a1 \\= 11-3 \\= 8\\\\nth term is 107 (given)\\\\Tn = 107\\\\a1+(n-1)d = 107\\\\3+(n-1)8 = 107\\\\n-1 = 104/8 \\= 13\\\\=> n = 14Now,20th term\\\\T20 = a1+19d\\\\= 3+19×8 \\= 3 + 152 \\= 155$