Question

Q. 5th form of an orithmetic Sequence is 32 and ath term is 56. find 15th term?​

Answer 1

Question:-

5th term of an Arithmetic Sequence is 32 and 8th term is 56.Find 15th term?

SOluTioN:-

We know

$\boxed{\sf a_n=a+(n-1)d}$

$\\ \sf \longmapsto a_5=a+(5-1)d=32$

$\\ \bf \longmapsto a+4d=32\dots(1)$

$\\ \sf \longmapsto a_8=56$

$\\ \sf \longmapsto a+7d=56\dots(2)$

• substarcting both equations

$\\ \sf \longmapsto 4d-7d=32-56$

$\\ \sf \longmapsto -3d=-24$

$\\ \sf \longmapsto 3d=24$

$\\ \sf \longmapsto d=\dfrac{24}{3}$

$\\ \sf \longmapsto \boxed{\bf d=8}$

• Putting the value in eq(1)

$\\ \sf \longmapsto a+4d=32$

$\\ \sf \longmapsto a+4(8)=32$

$\\ \sf \longmapsto a+32=32$

$\\ \sf \longmapsto a=32-32$

$\\ \sf \longmapsto \boxed{\bf a=0}$

Now

$\\ \sf \longmapsto a_{15}=a+(15-1)d$

$\\ \sf \longmapsto a_{15}=0+14(8)$

$\\ \sf \longmapsto a_{15}=112$