The given sequence is an arithmetic sequence with a common difference that increases by 1 with each term. To find the nth term of an arithmetic sequence, you can use the formula: nth term = a + (n-1)d, where a is the first term, n is the term number, and d is the common difference. In this case, the first term (a) is 3 and the common difference (d) is increasing by 1, so the nth term would be 3 + (n-1)(n-1) = n^2 + 2.
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The nth term of the sequence is (n + 1)2 + 2.
each time the number increases by 8 and the original number was 3.This means that nth term = 3+(n-1)8ie. the fourth term 27 would be 3 + (4-1)x8 = 3+24 = 27
ans=102 HOW? 6,11,13,27,38,.... 6(+5),11(+7),13(+9),27(+11),38(+13),51(+15),66(+17),83(+19),102adding 5 to 6 gives 11 adding 7(two greater than previous one) gives 13...and so on... to find the nth term N squared +2
Subtract 2 from the sequence and the answer becomes obvious: 1, 4, 9, 16, 25,...,N2 Now, add the 2 back in: 3, 6, 11, 18, 27,...,(N2+2)
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