Question

determine the sum of first 35 term of an AP if t2=1 and t7=22

Answer 1

Answer:

To calculate the sum of th first 35 terms of an a.p., we'll apply the formula:

Sn = (t1+tn)*n/2

S35 = (t1+t35)*35/2

We know, the terms t2 and t7, so we'll calculate the first term and the common difference:

t2 = t1 + d

t7 = t1 + 6d

We'll subtract t2 from t7:

t7-t2 = t1+6d-t1-d

We'll eliminate like terms:

22-2 = 5d

20 = 5d

We'll divide by 5:

d = 4

We'll put d=4 into the first equation:

t1 + d = 2  

t1 + 4 = 2

t1 = 2-4

t1 = -2

Now, we can calculate t35:

t35 = t1 + 34*d

t35 = -2 + 34*4

t35 = -2 + 136

t35 = 134

S35 = (-2+134)*35/2

S35 = 132*35/2

S35 = 66*35

S35 = 2310

Answer 2

calculate the sum of th first 35 terms of an a.p. aplly the formula:

Sn = (t1+tn)*n/2

S35 = (t1+t35)*35/2

We know, the terms t2 and t7, so we'll calculate the first term and the common difference:

 t2 = t1 + d

t7 = t1 + 6d

We'll subtract t2 from t7:

t7-t2 = t1+6d-t1-d

We'll eliminate like terms:

22-2 = 5d

20 = 5d

We'll divide by 5:

d = 4

We'll put d=4 into the first equation:

t1 + d = 2

t1 + 4 = 2

t1 = 2-4

t1 = -2

Now, we can calculate t35:

t35 = t1 + 34*d

t35 = -2 + 34*4

t35 = -2 + 136

t35 = 134

S35 = (-2+134)*35/2

S35 = 132*35/2

S35 = 66*35

S35 = 2310