Question

Find a10 given that a7 = 6 and d = 3 in the arithmetic sequence.

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

★ Given :

$\sf{a_7 = 6}$

Common Difference (d) = 3

__________________________

★ To Find :

We have to find the value of $\sf{a_10}$.

We know that,

$\large{\implies{\boxed{\boxed{\sf{a_7 = a + 6d}}}}} \\ \\ \sf{→ 6 = a + 6(3)} \\ \\ \sf{→ 6 = a + 18} \\ \\ \sf{→ a = 6 - 18} \\ \\ \sf{→ a = -12} \\ \\ \Large{\star{\boxed{\sf{a = -12}}}}$

$\rule{200}{2}$

Now,

$\large{\implies{\boxed{\boxed{\sf{a_{10} = a + 9d}}}}} \\ \\ \sf{→ a_{10} = -12 + 9(3)} \\ \\ \sf{→ a_{10} = -12 + 27} \\ \\ \sf{→ a_{10} = 15} \\ \\ \Large{\star{\boxed{\sf{a_{10} = 15}}}}$

Answer 2

Step-by-step explanation:

a7=6 ,d=3

d= a8-a7

3=a8-6

a8=9

d= a9-a8

3=a9-9

a9=12

d=a10-a9

3=a10-12

a10=15