Question

The sum of first 7 term of an a.p. is 49 and that of first 17 term of it is 289. Find the sum of first n term

Answer 1

ANSWER:

$S_n = n^2$

GIVEN:

$S_7 = 49\\S_{17}=289$

FORMULA:

$S_n = n/2(2a + (n-1)d)$

EXPLANATION:

$S_7 = 7/2(2a + (7-1)d) \\ \\ 7(2a + 6d) = 98 \\ \\ 2a = 14 - 6d \\ \\ S_{17} = 17/2(2a + (17 - 1)d) \\ \\2a + 16d = 17(2) \\ \\ 2a = 34 - 16d \\ \\ Equate \: the \: 2a \\ \\ 14 - 6d = 34 - 16d \\ \\ 10d = 20 \\ \\ d = 2 \\ \\ Substitute \: d = 2 \: in \: 2a = 14 - 6d \\ \\ 2a = 14 - 12 \\ \\ 2a = 2 \\ \\ S_n = n/2(2 + (n - 1)2) \\ \\ S_n = n/2(2+(n-1)2)\\ \\ S_n = n(1+n-1)\\ \\S_n = n^2$

Answer 2

Refers to attachment ⚘⚘