Question

Find the sum of the first 22term of the AP :8,3,-2,........................​

Answer 1

Step-by-step explanation:

Answer:

-979

Step-by-step explanation:

AP : 8, 3, - 2, - 7,....., to 22 terms.

Here, we have ;

First term (a) = 8

Number of terms (n) = 22

Difference (d) = 3 - 8 = -5

Sum of n terms is given by formula :

\begin{gathered}\bf S_n = \frac{n}{2}[2a +(n-1)d] \\ \\ \bf S_{22} = \frac{22}{2}[2 \times 8+(22-1)(-5) ] \\ \\ \bf S_{22} = 11[16 + 21 \times (-5)] \\ \\ \bf S_{22}= 11[ 16 - 105] \\ \\ \bf S_{22}= 11 \times (-89)\\ \\ \red{\boxed{\bf S_{22} = - 979}}\end{gathered}Sn=2n[2a+(n−1)d]S22=222[2×8+(22−1)(−5)]S22=11[16+21×(−5)]S22=11[16−105]S22=11×(−89)S22=−979

Hence, the sum of the given AP is -979.

Answer 2

Step-by-step explanation:

Sum=n/2(2a+(n-1)d)

Here,

n=22

a=8

d=3-8

=-5

Putting the values in formula,

=22/2 (2•8+(22-1) (-5))

=11 (16+(21) (-5))

=11(16-105)

=11(-89)

= -979