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Here is the solution:
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Formula for AP : tn = t1 + (n - 1)d
Given that t2 = 2
2 = t1 + (2 - 1)d
2 = t1 + d
Given that t7 = 22:
22 = t1 + (7 - 1)d
22 = t1 + 6d
Solve t1 and d:
2 = t1 + d ------------- [ 1 ]
22 = t1 + 6d ------------- [ 2 ]
Equation [ 2 ] - [ 1 ] :
5d = 20
d = 20 ÷ 5 = 4
Substitute d = 4 into equation [ 1 ] :
2 = t1 + 4
t1 = -2
Find the AP:
tn = -2 + (n - 1)4
tn = -2 + 4n - 4
tn = 4n - 6
Find the 35th term:
tn = 4n - 6
t35 = 4(35) - 6
t35 = 134
Find the sum of the first 35 terms:
Sum = n/2 ( t1 + tn)
sum = 35/2 ( -2 + 134)
sum = 2310
Answer: The sum of the first 35 terms is 2310
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