Question

if 11th term is 65 and 21st term is 135, then find value of 31st term and sum of first 16 terms

Answer 1

Answer:

The thirty first term in an A.P is 215 and Sum of first 16 terms is 920

Step-by-step explanation:

In an A.P

t11 = 65

t21 = 135

To find: 31st term & Sum of first 16 terms

31st term:

t11 → a + 10d = 65

t21 → a + 20d = 135

By solving the above two equations,

d = 7 and a = 5 ( a is the first term and d is the common difference)

31st term, t31 = a + 30d

= 5 + 210

= 215

Sum of 16 terms:

S(n) = $\frac{n}{2} (2a + (n - 1)d)$

n = 16

S(n).= 8(10 + 105)

= 8 × 115

= 920