Question

Sum of 4,11,18,25,32,39,46,53,60,67,74,81

Answer 1

Answer:

Use calculator.

Step-by-step explanation:

4+11+18+25+32+39+46+53+60+67+74+81

Answer 2

Solution :

• First term of the AP = 4.

• Last term of the AP = 82.

Common difference :

We know the formula for common difference of an AP i.e,

$\boxed{\bf{d = a_{n} - a_{n - 1}}}$

Where :

• d = Common Difference
• a = Any term of the AP

Using the above equation and substituting the values in it, we get :

$:\implies \bf{d = a_{n} - a_{n - 1}}$

$:\implies \bf{d = a_{3} - a_{3 - 1}}$

$:\implies \bf{d = a_{3} - a_{2}}$

$:\implies \bf{d = 18 - 11}$

$:\implies \bf{d = 7}$

$\boxed{\therefore \bf{d = 7}}$

Hence the common difference of the AP is 7.

No. of terms of the AP :

We know the formula for nth term i.e,

$\boxed{\bf{t_{n} = a_{1} + (n - 1)d}}$

Where :

• tn = nth term.
• n = No. of terms.
• d = Common Difference
• a = First term

Using the above equation and substituting the values in it , we get :

$:\implies \bf{t_{n} = a_{1} + (n - 1)d}$

$:\implies \bf{81 = 4 + (n - 1)7}$

$:\implies \bf{81 - 4 = (n - 1)7}$

$:\implies \bf{77 = (n - 1)7}$

$:\implies \bf{\dfrac{77}{7} = n - 1}$

$:\implies \bf{11 = n - 1}$

$:\implies \bf{11 + 1 = n}$

$:\implies \bf{12 = n}$

$\boxed{\therefore \bf{n = 12}}$

Hence there are 12 terms in the AP.

Sum of the AP :

We know the formula for sum of APs.i.e,

$\boxed{\bf{s_{n} = \dfrac{n}{2}\bigg(a + l\bigg)}}$

Where :

• n = No. of terms
• a = First term
• l = last term
• s = Sum of terms

$:\implies \bf{s_{n} = \dfrac{n}{2}\bigg(a + l\bigg)}$

$:\implies \bf{s_{n} = \dfrac{12}{2}\bigg(4 + 81\bigg)}$

$:\implies \bf{s_{n} = \dfrac{12}{2} \times 85}$

$:\implies \bf{s_{n} = 6 \times 85}$

$:\implies \bf{s_{n} = 510}$

$\boxed{\therefore \bf{s_{n} = 510}}$

Hence the sum of the AP is 510.