Question

An arithmetic sequence has t1 = 3, t2 = 10. Find tn, Sn.

Answer 1

Answer:

see explanation

Step-by-step explanation:

the n th term of an arithmetic sequence is

$t_{n}$ = $t_{1}$ + (n - 1)d

given $t_{1}$ = 3 and $t_{2}$ = 10, then

$t_{2}$ = 3 + d = 10 ⇒ d = 10 - 3 = 7

$t_{n}$ = 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4

the sum to n terms of an arithmetic sequence is

$S_{n}$ = $\frac{n}{2}$[2$t_{1}$ + (n - 1)d ]

                        = $\frac{n}{2}$[(2 × 3) + 7(n - 1) ]

                        = $\frac{n}{2}$(6 + 7n - 7 )

                        = $\frac{n}{2}$(7n - 1)

                        = $\frac{7}{2}$ n² - $\frac{1}{2}$ n