Question

The 11th term of an arithmetic sequence is 75. Find the sum of first 21 terms of the sequence​

Answer 1

Answer:1575

Step-by-step explanation:

a11 = 75 => a+10d=75

Sn = n[2a+(n-1)d]/2

S21 = 21[2a+20d]/2 = 21*2(a+10d)/2 = 21(a+10d) = 21*75 = 1575.

Hope this helps you!

Answer 2

${ \bold{ \green{ \underline{ \underline{ Answer }} : - }}} \\ \\Sum = 1575 \\ \\ { \bold{ \green{ \underline{ \underline{step - by -step \: \: explanation }} : - }}} \\ \\ { \bold {\underline{ Given } : - }} \\ \\ { \bold{ \blue{ \: \: \: \: \: \: \: \: \: \: \: \: . \: \: 11 \: \: th \: \: term \: \: of \: \: a.p. = 75}}} \\ \\ { \bold{ \underline{ To \: \: find } : - }} \\ \\ { \bold{ \blue{ \: \: \: \: \: \: \: \: \: \: \: \: . \: \: sum \: \: of \: \: first \: \: 21 \: \: term \: \: of \: \: a.p.}}} \\ \\ { \bold{ \underline{ \red{solution}} : - }} \\ \\ { \bold{ \orange{ \implies \: \: 11 \: \: th \: \: term \: \: of \: \: a.p. = 75 }}} \\ \\ { \bold{ \orange{ \implies \: \: a + 10d = 75}}} \: \: \: \: \: \: \: \: \: \: .........(1) \\ \\ { \bold{ \orange{ \implies \: sum \: \: of \: \: first \: \: 21 \: \: term = \frac{n}{2}(2a + 20d) }}} \\ \\ { \bold{ \orange{ \implies \: sum = \frac{21}{2}(2)(a + 10d) }}} \\ \\ { \bold{ \blue{ \: \: \: \: \: \: . \: \: now \: \: use \: \: equation \: (1) \: - }}} \\ \\ { \bold{ \orange{ \implies \:sum = \frac{21}{2 } \times 2 \times 75}}} \\ \\ { \bold{ \orange{ \implies \: { \boxed{sum = 1575}}}}} \\ \\ \\{ \bold{ \red{ { \huge{\underline{used \: \: formula} : - }}}}} \\ \\ { \bold{ \blue{ \: \: (1) \: \: T_{n} = a + (n - 1)d}}} \\ \\ { \bold{ \blue{ \: \: (2) \: \:sum \: \: of \: \: a.p. = \frac{n}{2} [2a + (n - 1)d]}}}$