Question

if the sum of the third and the 8th term of an ap is 7 and the sum of the 7th and the 14 terms is a -3 find the 10th term please ​

Answer 1

Answer:

Step-by-step explanation:

a3 + a8 = 7

a+2d + a+7d=7

2a+9d=7. - eqn1

a7+a14=-3

a+6d a+13d=-3

2a+19d=-3. -eqn2

eliminate eqn 1 & 2

2a+19d=-3

2a+9d=7

-. - -

10d=-10

d=-1

2a+9d=7

2a-9=7

a=8

a10= a+9d

= 8-9

=-1

hence proved

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Answer 2

Answer:

From the question, it seems like you know the last term of the Arithmetic Progression (AP).

Let it be an. Let the common difference (CD) be d1.

Let there be a new AP where the first term of the AP is A1=an. The new CD is d2=(−d1)

Then the sum of first m terms of the new AP will be the same as sum of m terms of the original AP from the end.

Apply the formula of sum of AP:

Sumn-terms=no. of terms2(2×first term of AP+(no.of terms−1)×Common difference of AP)

What you get is:

Summ=m2(2×A1+(m−1)d2)=m2[2×an+(m−1)(−d1)]=m2[2×an−(m−1)d1]