Question

2. Find the sum of first 22 terms of an AP whose second and fourth terms are 32 and 28
respectively.​

Answer 1

Given :-

• Second term = 32
• Fourth term = 28

To find :-

• Sum of first 22 terms

Solution :-

As we know that

Tn = a + (n - 1)d

Similarly

t2 = 32 = a + (2 - 1)d = a + d ...... eq 1

t4 = 28 = a + (4 - 1)d = a + 3d …… eq 2

Now , eq 2 - 1

28 - 32 = a + 3d - (a + d)

- 4 = a + 3d - a - d

- 4 = 2d

d = - 4/2

Common difference = - 2

Now , substituting d = - 2 in eq 1 & finding first term (a)

• a + d = 32

• a + (-2) = 32

• a - 2 = 32

• a = 32 + 2

• a = 34

Now , finding Sum of first 22 terms (S22)

Using formula

♦ Sn = n/2[2a + (n - 1)d]

→ S22 = 22/2[2(34) + (22 - 1)(-2)]

→ S22 = 11[68 + (21)(-2)]

→ S22 = 11[68 - 42]

→ S22 = 11[26]

→ S22 = 286

Hence , sum of 22 terms = 286.