Question

Please tell the solution ​

Answer 1

Answer:

176

Step-by-step explanation:

Let for the A.P. , a = 1st term and common difference = d

then nth term, T(n)= a + (n-1)d

$\frac{2n + 1}{3} = a + (n - 1)d$

$= > 2n + 1 = 3a + 3d(n - 1)$

$2n + 1 = {3a - 3d} + {3nd}$

On comparing LHS and RHS, we get

$2n = 3dn$

$2 = 3d$

$d = \frac{2}{3} ..........................(1)$

and

$3a - 3d = 1$

putting value from (1), we get

$3a - 3 \times \frac{2}{3} = 1$

$3a - 2 = 1$

$3a = 3 \\ = > a = 1$

hence sum of 22 terms is

S(22)

$= \frac{22}{2} \times ({2 + 14} )= 11 \times 16 = 176$