Question

11th term of an arithmetic sequence is 26 .

a) What is the sum of first and 21st terms of this sequence ?

b) What is the sum of first 21 terms of this sequence​

Answer 1

$\mathfrak{\huge \underline{Question:}}$

11th term of an arithmetic sequence is 26 .

a) What is the sum of first and 21st terms of this sequence ?

b) What is the sum of first 21 terms of this sequence

$\mathfrak{\huge \underline{Given:}}$

Let the first term be a and common difference be d

$T_{11} = a+(11-1)d \\\\\sf = a+10d=26 (given)$

$\mathfrak{\huge \underline{Solution:}}$

a) Sum of first and 21st term

= a+[a+(21-1)d]

= 2a+20d

= 2(a+10d)

= 2x 26 = 52

b) Use following formula

$\boxed{\frac{n}{2}[2a+(n-1)d]}$

$\sf =\frac{21}{2}[2a+20d] \\\\\sf \frac{21}{2}x2(a+10d) \\\\\sf \frac{21}{\cancel{2}}x \cancel{2} (a+10d) \\\\\sf =21 x 26 = 546$