Question

In an arithmetic series t6 = −4, t10 = −12. Find S10.

Answer 1

Answer:

$S_{10}$ = - 30

Step-by-step explanation:

For a given arithmetic sequence the n th term formula is

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

where d is the common difference and $t_{1}$ the first term

We have to find d and $t_{1}$

from the given information we can write 2 equations and solve for d and $t_{1}$

$t_{6}$ = $t_{1}$ + 5d = - 4 → (1)

$t_{10}$ = $t_{1}$ + 9d = - 12 → (2)

subtract (1) from (2) term by term

4d = - 8 ⇒ d = - 2

substitute d = - 2 in (1)

$t_{1}$ - 10 = - 4 ⇒ $t_{1}$ = - 4 + 10 = 6

The sum to n terms of an arithmetic sequence is

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

$S_{10}$ = 5[(2 × 6) + (9 × - 2) ] = 5(12 - 18) = 5 × - 6 = - 30