Math Questions Series, Sequences, and Sums?

it is geometric. the ratio is -1/3

so as you comprehend, the final term of an arithmetic progression is a + id, the place a is the beginning term and d is the easy distinction. With that throughout the time of recommendations, enable's resolve Q1: Expressed in terms of a and d, the 1st 2 words are a and a+d. So their sum could be a + (a+d) = 2a+d. So we get one equation via placing 2a+d to 40 seven i.e. 2a + d = 40 seven --- (a million) next, the thirtieth term is a + (30-a million)d = a +29d, which we set to -sixty two i.e. a + 29d = -sixty two --- (2) So we've a pair of simultaneous equations which we can resolve to get a and d. With Q2, first % out the arithmetic progression you may desire to sum. the 1st quantity in a million ... 4 hundred it particularly is divisible via 3 could be 3. The very final quantity divisible via 3 could be 399. So your arithmetic progression sounds like this: 3, 6, 9, 12, ... ,399 To sum this sequence, in basic terms word which you will ingredient out 3 from the progression so as that the needed sum is in basic terms thrice (a million+2+3+...+133). The latter sum is in basic terms 133(133+a million)/2 = 8911. Multiplying via 3 we get 26733.