Question

if 2 term of ap is 2 and 7 term is 22 find they sum of 35terms​

Answer 1

Step-by-step explanation:

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Answer 2

Let a and d be the first term and common difference respectively of the above AP

Given

• Second term is 2
• Seventh term is 22

To finD

Sum of 35 terms

ATQ,

a + d = 2__________(1)

a + 6d = 22_________(2)

From equation (1),

a = 2 - d

Implies,

» 2 - d + 6d = 22

» 5d = 20

» d = 4

Common Difference of the AP is 4

Also,

a = 2 - d

» a = 2 - 4

» a = - 2

First Term of the AP is - 2

Now,

Sum of 35 terms would be (n = 35)

$\sf \: s = \dfrac{n}{2} \bigg(2a + (n - 1)d \bigg) \\ \\ \longrightarrow \: \sf \: s = \frac{35}{2} \bigg(2( - 2) + 34 \times 4 \bigg) \\ \\ \longrightarrow \: \sf \: s = \dfrac{35}{2} \times 132 \\ \\ \longrightarrow \: \boxed{ \boxed{ \sf \: s = 2310}}$

Sum of the terms is 2310