Question

If 6 term of an ap is -10 and 10th term is minus 26 then find the 15th term

Answer 1

Given:-

→a⁶=-10

→a¹⁰=-26

$\rule{200}{1}$

To find:-

→The 15th Term, i.e= a¹⁵=?

$\rule{200}{1}$

Answer:-

๛Using formula๛

→aⁿ=a+(n-1)d

→a⁶=a+(6-1)d=-10

→a⁶=a+5d=-10–·(1)

→a¹⁰=a+(10-1)d=-26

→a10=a+9d=-26–·(2)

♦Subtract (1)&(2)♦

→a+5d=-10

→a+9d=-26

★Signs Changed★

→-4d=16

→d=$\frac{\cancel{16}}{\cancel{-4}}$

→d=-4–·(3)

♠Using (3) in (1)♠

→a+5×-4=-10

→a-20=-10

→a=-10+20

→a=10–·(4)

♦Using (3)&(4)♦

→a¹⁵=a+(15-1)d

→a¹⁵=10+14×-4

→a¹⁵=10-56

→a¹⁵=-46

•Hence 15ᵗʰ Term is -46•

$\rule{200}{2}$

Answer 2

$</p><p>a_{6} = -10 \\ \\ a_{10} = -26\\ \\ =>d = -4\\ \\ =>a = 10 \\ \\ a_{15} = -50$