Question

12. Find the sum of first 22 terms of an A.P. 8,3,-2......
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Answer 1

• Sum of 22 terms of A.P is -979

Step-by-step explanation:

To find:-

• Sum of 22 terms of A.P 8, 3, -2 .......

Solution:-

Our A.P is,

8, 3, -2 ......

First term = 8

Common difference = a₂ - a₁

= 3 - 8

= - 5

Common difference = -5 .

We know that,

$\boxed{ \star \sf \: \bold{S_{n} = \cfrac{n}{2}[2a + (n -1)d]}}$

In which,

• n is number of terms of A.P .
• a is first term of A.P .
• d is common difference of A.P .

n = 22 terms

a = 8

d = -5

Put value of a, n and d in formula :

$\longrightarrow \sf S_{22} = \cfrac{22}{2} [2 \times 8 + (2 - 1) \times ( - 5)]$

$\longrightarrow \sf S_{22} = 11[16 + (21) \times ( - 5)]$

$\longrightarrow \sf S_{22} = 11[16 + ( - 105)]$

$\longrightarrow \sf S_{22} =11 \times [- 89]$

$\longrightarrow \sf S_{22} = - 979$

Therefore,

Sum of 22 terms of A.P is -979 .