Question

find the sum of all multiples of 7 lying between 500 and 900

Answer 1

$heya \: mate \\ \\ here \: is \: your \: answer \\ \\ 504 \: 511 \: 518... \: 889 \: 896 \: are \: \\ multiplies \: of \: 7 \: between \: \\ 500 - 900 \\ and \: these \: are \: in \: arithmetic \: \\ progress \\ the \: first \: term \: a = 504 \\ \: the \: common \: difference \: is \: \\ a2 - a1 = d \\ d = 511 - 504 = 7 \\ let \: the \: number \: of \: term \: = n \\ last \: term \: = 896 \\ we \: know \: this \: formula \\ a + (n - 1) \times d = last \: term \\ \\ 504 + (n - 1) \times 7 = 896 \\ divide \: each \: term \: with \: \: seven \: \\ 72 + n - 1 = 128 \\ 71 + n = 128 \\ n = 128 - 71 = 57 \: therefore \\ sums \: of \: n \: term \\ sn = \frac{n}{2} (a + l) \\ the \: sum \: of \: 57 \: term \\ \\ s57 = \frac{57}{2} (504 + 896) \\ = \frac{57}{2} (1400) \\ 57 \times 700 = 39900 \\ \\ the \: sum \: of \: 7 \: multiplies \: between \: 500 \: and \\ \\ 900 = 39900$

Answer 2

Answer:

Step-by-step explanation: