Question

If the 1st term of a series is 7 and 13th term is 35. Find the sum of 13 terms of the sequence.

Answer 1

Given a = 7, a₁₃ = 35

We find to find d

We know that

a_n = a + (n - 1)d

Putting a = 7, n = 13 and a_n = 35

35 = 7 + (13 - 1) x d

35 = 7 + 12d

35 - 7 = 12d

28 = 12 d

\(\frac{28}{12}=d\)

\(\frac73=d\)

d =  \(\frac73\) 

Now we need to find S₁₃

We can use formula

S_n = \(\frac n2(a+l)\)

Putting n = 13, a = 7, a₁₃ = 35

 = \(\frac{13}2\)(7 + 35)

 = \(\frac{13}2\) x 42

 = 13 x 21

 = 273