Question

determine the sum of first 35 terms of an A.P. if 2nd term is 2 and 7th term is 22

Answer 1

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Answer 2

Answer:

2310

Step-by-step explanation:

Given : 2nd term is 2 and 7th term is 22

To Find :Determine the sum of first 35 terms of an A.P.

Solution:

Formula of nth term of AP = $a_n=a+(n-1)d$

Substitute n = 2

$a_{2}=a+(2-1)d$

Since we are given that 2nd term is 2

So, $a_{2}=a+d=2$   -----1

Substitute n = 7

$a_{7}=a+(7-1)d$

Since we are given that 7th term is 22

So, $a_{7}=a+6d=22$   -----2

Subtract 1 from 2

$a+6d-a-d=22-2$

$5d=20$

$d=\frac{20}{5}$

$d=4$

Substitute d in 1

$a+4=2$  

$a=-2$  

Formula of sum of first n terms = $S_n=\frac{n}{2}(2a+(n-1)d)$

Substitute n = 35

$S_{35}=\frac{35}{2}(2(-2)+(35-1)4)$

$S_{35}=2310$

Hence  the sum of first 35 terms of an A.P. is 2310.