Question

Find the sum of the first 22 terms of the AP : 8, 3, –2, . . .

Answer 1

Answer:

• Sum of 22 terms = -979

Given:

• AP: 8, 3, -2, ...

To Find:

• Sum of first 22 terms

Steps:

From the given AP, we can see that:

• First term (a) = 8
• Common difference (d) = -5
• Number of terms = 22

The formula for calculating the sum of 'n' terms in an AP is:

$\boxed{ Sum\:\:(S_{(n)}) = \dfrac{n}{2}\: [\:2a + (n-1)d\: ]}$

Substituting the given information we get:

$\implies S_{22} = \dfrac{22}{2} \: [\: 2(8) + (22 - 1) (-5) \:]\\\\\\\implies S_{22} = 11\:[\:16 + ( 21 \times (-5))\:]\\\\\\\implies S_{22} = 11\:[\: 16 - 105\:]\\\\\\\implies S_{22} = 11 \times -89\\\\\\\implies \boxed{S_{22} = -979}$

Hence the sum of first 22 terms of the AP is -979.